Combination of Resistors in Series and Parallel · Combination of Resistors in Series and Parallel...
Transcript of Combination of Resistors in Series and Parallel · Combination of Resistors in Series and Parallel...
Combination of Resistors in Series and Parallel
An important part of electric circuits is Resistors. When a resistor
connects to a combination of series and parallel connection it forms
more complex circuit networks. Regulation of the current level of a
device is a resistor’s functionality. To know more about resistors in
series or parallel, let’s explore the article further!
Introduction
Resistors are two-terminal devices. Therefore, voltage division,
regulation of current in the device and adjusting signal level are the
functionality of a resistor. Representation of a resistor is done through
Ohm’s Law.
R =
V
I
Many types of resistors are available and some are the following:
1. Wire-wound resistor.
2. Semi-conductor resistor.
3. Flim resistor.
4. Carbon Composition resistor.
Resistor in Series
In this kind of connection, resistors are in a sequential array of
resistors to form an electronic circuit/ device. Resistors are connected
is in a single line and hence common current flows in the circuit.
The connection is in such a manner that the current flowing through
the 1st register has to then flow further through the 2nd register and
then through 3rd. Therefore, a common current is flowing in
connection with a resistor in series. At all point in the circuit, the
current amoung the resistors is same. For example,
I1 = I2 = I3 = It = 2ma
All the resistors in series that is R1, R2, R3 have current I1, I2, I3
respectively and the current of the circuit is It.
As resistors are connected in series the sum of the individual resistor
is equal to the total resistance of the circuit. Let R1, R2, R3 be the
resistors connected in series and Rt be the total resistance of the
circuit. so the total resistance of the circuit that is 12Ω, is the sum of
all individual resistors R1, R2, R3 having 6KΩ, 4KΩ, 2KΩ
respectively.
This circuit of the resistors in series can also be represented by
Therefore, the total resistance can be calculated as
R1 + R2 + R3 = Rt
furthermore, the total resistance of the above resistors in series is
given by
Rt = 6KΩ + 4KΩ + 2KΩ = 12KΩ
The Equation of Resistors in Series
Since the connection of resistor is in a series fashion that is in the
sequential array or continuously one after other. The total resistance is
equal to the resistance value of each resistor in the device/ circuit.
R1+R2+R3+R4+………………….Rn=Rt
where R is the resistance of the resistor and Rn represents the resistor
number or the total resistance value.
Resistor in Parallel
In this kind of connection, the terminals of resistors are connected to
the same terminal of the other resistor to form an electronic circuit/
device. Resistors are connected is in parallel fashion and hence
common voltage drop in the circuit.
Unlike, series connection, in parallel connection, current can have
multiple paths to flow through the circuit, hence parallel connection is
also current dividers. Common voltage drop is across the parallelly
connected circuits/networks. At the terminals of the circuit, the
voltage drop is always the same. For example
VR1=VR2=VR3=VRT=14V
The voltage across R1 is equal to the voltage across R2 and similarly,
equal to R3 and hence the total voltage drop is equal to the voltage
across the circuit. Reciprocal of individual resistance of each resistor
and the sum of all the reciprocated resistance of resistor will us the
total resistance of the circuit.
1
(
R
t
)
=
1
(
R
1
)
+
1
(
R
2
)
+
1
(
R
3
)
+…………
1
(
R
n
)
Questions For You
Q1: When three identical resistances are connected to form a triangle
the resultant resistance between any two corners is 30Ω .The value of
each resistance is:
1. 90Ω54Ω
2. 15Ω
3. 45Ω
Answer. 45Ω. 1/RAB=1/2R+1/R=2R3=30
RAB=3R/2=3*30/2
⇒R=45Ω
Q2. Identify the changes in a circuit on adding a light bulb in parallel
to the actual resistance of the circuit. It will:
● decrease the total resistance
● increase the total resistance
● make the voltage lost in each light bulb different
● make the current through each light bulb the same
● not change the total current through the circuit
Answer. decrease the total resistance. For a parallel combination of
two resistances,
1/Req=1/R1+1/R2
⟹Req< min {R1, the R2}
A light bulb has its own resistance and hence the total resistance of the
circuit decreases when it is connected in parallel to the actual
resistance of the circuit.
Q3.The least resistance that one can have from six resistors of each 0.1 ohm
resistance is:
1. 0.167 Ω
2. 0.00167 Ω
3. 1.67 Ω
Answer. 1.67 Ω. Least resistance is possible when all are in parallel.
⇒Req=R/6=0.16=0.0167 Ω
Ohm’s Law
Whenever the fan in your room is on and when you feel cold you
reduce the fan’s speed. For doing so you use the speed control knob
on the switchboard. But how does the knob work? What’s its
mechanism? The knob works on the principles of ‘Ohm’s Law’. But
what does Ohm’s law of current electricity state? Let us study Ohm’s
law of current electricity.
Ohm’s Law of Current Electricity
Ohm’s Law of Current Electricity is named after the scientist ”Ohm”.
Most basic components of current electricity are voltage, current, and
resistance. Ohm’s law shows a simple relation between these three
quantities.
Ohm’s law of current electricity states that the current flowing in a
conductor is directly proportional to the potential difference across its
ends provided the physical conditions and temperature of the
conductor remains constant.
Voltage= Current× Resistance
V= I×R
where V= voltage, I= current and R= resistance. The SI unit of
resistance is ohms and is denoted by Ω. In order to establish the
current-voltage relationship, the ratio V / I remains constant for a
given resistance, therefore a graph between the potential difference(V)
and the current (I) must be a straight line.
This law helps us in determining either voltage, current or impedance
or resistance of a linear electric circuit when the other two quantities
are known to us. It also makes power calculation simpler.
Limitations of Ohm’s Law of Current Electricity
● The law is not applicable to unilateral networks. Unilateral
networks allow the current to flow in one direction. Such types
of network consist of elements like a diode, transistor, etc.
● Ohm’s law is also not applicable to non – linear elements.
Non-linear elements are those which do not have current
exactly proportional to the applied voltage that means the
resistance value of those elements changes for different values
of voltage and current. Examples of non – linear elements are
the thyristor.
● The relation between V and I depends on the sign of V. In other
words, if I is the current for a certain V, then reversing the
direction of V keeping its magnitude fixed, does not produce a
current of the same magnitude as I in the opposite direction.
This happens for example in the case of a diode.
How do we find the unknown Values of Resistance?
It is the constant ratio that gives the unknown values of resistance. For
a wire of uniform cross-section, the resistance depends on the length l
and the area of cross-section A. It also depends on the temperature of
the conductor. At a given temperature the resistance,
R =
ρl
A
where ρ is the specific resistance or resistivity and is characteristic of
the material of wire. Using the last equation,
V = I × R =
Iρl
A
I/A is called the current density and is denoted by j. The SI unit of
current density is A/m². So,
E I = j ρ I
This can be written as E = j ρ or j = σ E, where σ is 1/ρ is
conductivity.
Solved Questions for You
Q1. The unit for electric conductivity is
A. per ohm per cm
B. ohm × cm
C. ohm per second
D. who
Solution: A. We know that R =
Iρl
A
. R has dimensions of an ohm, L has dimensions of length A has
dimensions of (length)². Therefore, ρ has dimensions of ohm-cm.
Q2. What will happen to the current passing through a resistance, if
the potential difference across it is doubled and the resistance is
halved?
A. Remains unchanged
B. Becomes double
C. Becomes half
D. It becomes four times.
Solution: A. Using ohm’s law
I =
V
R
I’ =
2V
R/2
so, I’ = 4I
Hence the current becomes four times.
Electrical Energy and Power
Surely you have faced a situation where some important appliance
stops working because the cells run out. What does that mean? That
means the cell is no more able to give current or we can say that it has
no more energy stored. This means that the energy that is the
chemical energy is consumed in the electric circuits. So in order to
find out the amount of energy consumed, we study the electric energy
or electric power.
Electric Energy
To under the concept of electric energy, let us consider a conductor
carrying the current I and potential difference V between the two
endpoints A and B. Let us denoted the electric potential of A and B as
V(A) and V(B). As we know that current is flowing from A to B so
V(A) >V(B) and the potential difference across AB is V = V(A) –
V(B) > 0
NOW, in a time interval Δt, an amount of charge ΔQ is equal to IΔt
moves from point A to B of the circuit and the work was done by the
electric field is equal to the product of V and ΔQ.
Here if the charges in the conductor move without collisions, their
kinetic energy would also change. Conservation of total energy is ΔK
= I V Δt > 0. The amount of energy dissipated as heat in a conductor
in a time interval Δt is,
ΔW = V ΔQ = VI Δt
Electric Power
The rate at which the electric energy enters the portion of the circuit is
called the electrical power input. The rate at which work is done in
bringing the charged particles from one point to another is known as
electric power. It is denoted by P.
The SI unit of power is watt (W). One watt is the power consumed by
the device catting 1A of current when operated at a potential
difference of 1 V.
P = VI
Applying ohms law we can write
P = I² R = V²/R
The above equation is the power loss in a conductor of resistance R
which carries the current I. The application of electrical power is that
it is transmitted from the power stations which later on reaches our
homes and the industrial factories via transmission cables.
Now we know that the transmission of power is very costly. So how
do we minimize the power loss in transmission cables? Let us consider
a device R to which a power is to be delivered via the cables having
resistance Rc. So if V is the voltage across R and current I then,
P = V I
The wires which are connected to the device from the power station
has finite resistance Rc. So, Pc = I² Rc
∴ P² Rc / V²
Hence the power wasted in connecting the wires is inversely
proportional to V². So the resistance Rc of the transmission cable is
considerable.
Solved Questions
Q1. The circuit given below is for the operation of an industrial fan.
The resistance of the fan is 30 ohm. The regulator provided with the
fan is a fixed resistor and a variable resistor in parallel. Under what
value of the variable resistance given, power transferred to the fans
will be maximum? The power source of the fan is a dc source with an
internal resistance of 60 oh.
A. 3 0HM
B. 0
C. ∞
D. 6 ohm
Solution: The correct option is “B”. The power which transfers to the
fan is P = V²/R where R is the total resistance of the circuit. As power
is inversely proportional to total resistance. So for maximum power,
the total resistance should be minimum. Total resistance here is R =
6r/6 +r + 3. r is the variable resistance. R is minimum when r = 0
Q2. An electric heater has a resistance of 150 ohms and can bear a
maximum current of 1 ampere. If we use the heater on 220-volt mains, the
least resistance required in the circuit will be
A. 70 ohms
B. 5 ohms
C. 2.5 ohms
D. 1.4 ohms
Solution: The correct option is “A”. Given that the heater can bear a
maximum current of 1 ampere we need to add a resistance to the
circuit in series with the heater so that current is less or equal to 1
ampere. Let that resistance be R, then (150+ R) × 1 = 220. R = 70
ohm.
Resistivity of Various Materials
You must have had electric shocks! Haven’t you? Did you get the
shock on a plastic wire? It is not possible. You can’t get shocks from
plastic wires. But, why is it so? It is because of a phenomenon that we
will read about in this chapter. We will study about resistivity of
various materials.
What is Resistance?
We know that electric current that flows in a circuit is as similar to the
water flowing through a river. In a river rock, branches and other
particles resist the flow of water. in a very similar fashion, a circuit
has elements to resist the flow of electrons.
Resistance is nothing but this property of resisting the flow of
electrons or the current. The unit of resistance is ohm. One ohm is
equal to volt per ampere. From Ohm’s law, we have seen that R = V /
I, Where V is the voltage and I is the current.
Resistors are used to resist or control the flow of electrons by the
conductive material. They do not provide any power to the circuit.
They may reduce the voltage and current passing through the circuit.
Hence, resistors are passive devices. Most of the resistors are made up
of carbon, metal or metal oxide film.
Resistivity
Resistivity is the resistance per unit length and cross-sectional area. It
is the property of the material that opposes the flow of charge or the
flow of electric current. The unit of resistivity is ohm meter.
We know that R = ρ L / A. Thus we can derive the expression for
resistivity from this formula. ρ = R A / L, where R is the resistance in
ohms, A is the area of cross-section in square meters and L is the
length in meters. When the values of L, the length, and A, the area is
equal to one, we can say that the resistivity is equal to the resistance.
So, resistivity is the specific resistance of a material. When we have a
thick wire, the resistance decreases. The resistance increases when the
wire is thin as the area of cross-section is less. When the length of the
wire increases, the resistance also increases. When the length of the
wire decreases, the resistance decreases as the length is less.
The Resistivity of Various Materials
A material with high resistivity means it has got high resistance and
will resist the flow of electrons. A material with low resistivity means
it has low resistance and thus the electrons flow smoothly through the
material.
For example, Copper and Aluminium have low resistivity. Good
conductors have less resistivity. Insulators have a high resistivity. The
resistivity of semiconductors lies between conductors and insulators.
Gold is a good conductor of electricity and so it has low resistivity.
The glass is a good insulator which does not allow the flow of
electrons. Hence, it has a high resistivity. Silicon is a semiconductor
and so it allows partial movements of electrons. The Resistivity of
Silicon comes between glass and gold. The resistivity for perfect
conductors is zero and the resistivity for perfect insulators is infinite.
Solved Examples for You
Question 1: The resistivity of alloys is ______ than its constituent
elements.
A. Higher
B. Lower
C. Same
D. None
Answer: Option A – Higher. Metal alloy has a greater resistivity than
the corresponding metals because of lattice distortion from the
alloying elements. A metal with no alloying elements would transport
electron by drift oscillation over the lattice.
The difference in atomic radii of alloying elements and in
electronegativity from base metal, the presence of alloying element
changes the local electronic structure of the base metal. Such change
modulates the typical drift oscillation mechanism in electron
conduction by scattering and leads to higher resistance.
Question 2: Name three materials or substances that have good
resistance.
Answer: Insulators have good resistance. Examples include glass,
ceramics, wood etc.
Temperature Dependence of Resistivity
Resistivity is the nature of a material that allows or resists the flow of
electric current through a given element or material. What is
surprising about resistivity is the temperature dependence of electrical
resistance! It is hard to comprehend how the temperature of an
element can affect the degree of conductance of such material but
believe it or not, this is the world of science and it happens almost
every day, all around us!
The Concept of Electrical Resistance
Resistivity is the phenomenon of specific electrical resistance of a
material or volume resistivity of a material. It can also be defined as
the intrinsic property of a material that displays how the material
resists the flow of current in the material. The concept can also be
defined as the resistance that is displayed by a conductor which has
unit length and unit area of the given cross section.
So resistivity is not dependent upon the length and area of a
cross-section of a given material. However, the resistance of a
material depends upon the length and area of the cross-section of the
material in question. The resistivity manifests as:
ρ = RA/L,
where R is the resistance in ohms, A is the area of cross-section in
square meters and L is the length in meters. The unit of resistivity is
universally accepted as ohm-meter.
The Concept of Temperature Resistivity
The resistivity of materials is dependent upon the temperature of the
material.
ρt = ρ0 [1 + α (T – T0)]
is the equation that defines the connection between the temperature
and the resistivity of a given material. In this equation ρ0 is the
resistivity at an equilibrium temperature, ρt is the resistivity at t0 C, T0
is referred to as the reference temperature and α is the temperature
coefficient of resistivity.
Understanding the Equation
It is known that an electric current is the movement of free electrons
from one atom to the other when there is a potential difference
between the two. In the case of conductors, no gap is present between
the conduction band and valence band of the electrons. In most cases,
these bands overlap each other.
The valence electrons in a given atom are loosely bound to the nucleus
in a conducting material. Quite often, metals or conductors have a low
ionization energy and therefore, they tend to lose electrons very
fluidly. When an electric current is applied, the electrons are free to
move within the structure on their own. This happens in the case of
the normal temperature of a material.
However, when the temperature increases gradually, the vibrations in
the metal ions in the lattice structure also undergo an increase. In this
case, the atoms begin to vibrate with a higher amplitude. Such
vibrations, in turn, cause frequent collisions between the free electrons
and the remaining electrons.
Each such collision drains out some degree of energy of the free
moving electrons and renders them in a condition in which they are
not able to move. Thus, it causes a restriction in the movement of the
delocalized electrons.
In the case of metals or conductors, it is rightly said that they hold a
positive temperature coefficient. The value α is positive. For most of
the metals, the resistivity increases in a linear pattern with an increase
in the temperature in a range of 500K.
What happens in Insulators?
In the case of insulators, the forbidden energy gap between the
conduction band and the valence band is very high. The valence band
is filled with the electrons of the atoms. Diamond is a unique example
of an insulator. Here, all the valence electrons are involved in the
covalent bond formation and as a result, conduction does not take
place. The electrons are too tightly bound to the nucleus of the atom.
Solved Examples for You
Question: State the properties and features of temperature resistivity in
conductors and insulators.
Solution: The resistivity of a material is defined as the resistance
offered by a conductor having a given unit length and unit area of
cross-section. The unit of resistivity is ohm meter. The formula for
deriving resistivity is ρ = RA/L. Here, R is the resistance in ohms, A is
the area of cross-section in square meters and L is the length in
meters.
● In the case of metals or conductors, when the temperature
increases, the resistivity of the metal increases as a result. Thus,
the flow of current in the metal decreases. This phenomenon
reflects a positive temperature coefficient. The value α is
positive in this case.
● In the case of insulators, the conductivity of the material
generally increases, when the temperature is made to increase.
When the conductivity of the material undergoes an increase, it
is easy to decipher that the resistivity of the material decreases
and the current flow of the material increases.
Drift of Electrons and the Origin of Resistivity
What is resistance? The property of the material to oppose the electric
current is known as resistivity. It is inversely proportional to the drift
of electrons. To more about drift of electrons and resistivity, let’s
explore the article further to know what is resistance, the drift of
electrons and the origin of resistivity!
Introduction
The net velocity of the circuit is zero when electrons move randomly
in the circuit and electric field is not applied to the circuit. Drift force
is the force driving the electrons through a conductor and the force
opposing the drift force is resistivity.
What is Resistance or Resistivity?
The tendency of a material/device towards resistance is the resistivity
of the device/circuit. The SI unit of resistivity is ohm-meter. The unit
length across the cross-sectional area of the device is also resistivity.
Therefore, the nature and temperature of the material also define
resistivity (σ).
σ= [Math Processing Error]
The graph of resistivity as follows. The graphs depict current (I) to
voltage (V) ratio, whereas, dotted line A, B, C shows the idealized
graph. After a certain amount of current, the device starts resisting to
the current flowing in the system and the resistivity becomes constant.
Drift of Electrons
The free electrons in a conductor have random velocities and move in
random directions. When current is applied across the conductor the
randomly moving electrons are subjected to electrical forces along the
direction of the electric field.
Due to this electric field, free electrons still have their random moving
nature, but they will move through the conductor with a certain along
with force. The net velocity in a conductor due to the moving of
electrons is referred to as the drift of electrons.
Drift Velocity = \( \frac {Current} {(no.of free Electrons )*(Area of
conductor)*(Charge of Eletrons)} \)
Vd=I/(A*n*e)
For example, let’s say you are crossing a river and moving from one
bank to another bank along with the river flow, then you are the
electron which is randomly moving and river water acts as the drift
force. Then the force applied to the randomly moving electron will
result in the change of course of the path of an electron.
Examples for You on What is Resistance!
Question 1: When a potential difference V is applied across a
conductor at a temperature T, the drift velocity of electrons is
proportional to
a. √V
b. V
c. √T
d. T
Solution: V. We know that Drift velocity vd ∝ E ∝ (Vl) (∵E=Vl), so
for a particular conductor of a particular length, the drift velocity will
directly depend upon the voltage. Hence vd∝V.
Question 2: A steady current flows in a metallic conductor of
non-uniform cross-section. Which of the following quantities is
constant along the conductor?
a. Drift speed
b. Current
c. Currently density
d. None of these
Solution: Current. When a steady current flows through a metallic
conductor of non-uniform cross-section, then drift velocity
Vd=I/(Ane) or Vd∞(1/A). E∞(1/A). Both Vd and E change with A,
only current I remain constant.
Question 3: Relation between drift velocity (vd) of electron and
thermal velocity (vt) of an electron at room temp is expressed as
a. vd=vt
b. vd>vt
c. as vd<vt
d. vd=vt=0
Solution: vd<vt. Electrons with the Fermi energy carry considerable
kinetic energy. Their mean thermal velocity at temperature T should
be vt= √3kTm, which generally turns out to be quite large. The
average velocity with which electrons must pass along a conductor to
carry a current is called drift velocity is given by vd=I/(Ane) which is
much less than the thermal velocity. Hence vd<vt.
Atmospheric Electricity and Kirchhoff’s Law
Some relationship between current and voltage does exist in an
electrical circuit network. Kirchhoff’s Law helps us in solving these
relations and also help us understand those. This set of rules helps us
in solving many complex circuits, for this reason, explore the article to
know more about the Law!
Atmospheric Electricity
The global atmospheric electrical circuit is the relation between the
Earth’s surface, ionosphere, and the atmosphere. Atmospheric
electricity is the regular result of the peak results in earth’s
electromagnetic network. The induction of EArth’s surface and other
electromagnetic devices is because of the free electricity present in the
air and the clouds.
The thunderstorm acts like the batteries of the atmosphere providing
the atmosphere with the charge it needs. The atmospheric electricity
charges the ionosphere up to 400,000 volts with respect to earth’s
surface. Lighting is caused due to electric discharge is proved by some
physicists experimenters.
Video on Current Electricity
Kirchhoff’s Law
In 1845, Gustav Kirchoff, a German physicist, developed a set of rules
and theorems. To deal with the conservation of energy and potential
difference within the circuit. Kirchhoff’s Law helps us in solving
complex relation between current and potential difference commonly
known as voltage. The 2 rules developed are Kirchhoff’s Current Law
and Kirchhoff’s Voltage Law. Electrical Engineering widely uses this
Law.
1. Kirchhoff’s Current Law
Kirchhoff’s Current rule, in other words, is Kirchhoff’s first Law,
Kirchhoff’s point rule or Kirchhoff’s junction rule. The principle of
conservation of electric charges states that: At any node ( junction ) in
an electrical circuit, the sum of all currents flowing into that node is
equal to the sum of currents flowing out of that node or equivalently.
If I1, I2, and I3 are current entering junction and I4 and I5 are current
leaving junction. Then the sun of all Current entering and leaving
junction is always zero, in the case of Kirchhoff’s Current Law.
I1+I2+I3-I4-I5=0
Adding all the Current entering junctions and subtracting all the
Current leaving junctions the Current Law is derived, as the result of
this equation, the result will always be Zero. Therefore, we conclude
Kirchhoff’s current Law or Kirchhoff’s First Law.
2. Kirchhoff’s Voltage Law
Kirchhoff’s Voltage Law, in other words, is Kirchhoff’s Second Law,
Kirchhoff’s loop (or mesh). The principle of conservation of energy
states that the directed sum of the electrical potential difference
(Voltage) around any closed network is zero. In other words, the sum
of all EMFs is equivalent to the sum the potential drops in the closed
electrical network.
The algebraic sum of the emf available in the closed loop electric
network is equivalent to the product of all the resistance of the
conductors and the current in the closed loop. In conclusion, the
circuit should have the sum of Voltage drop to zero.
Solved Examples for You
Question 1: The layer of the earth’s atmosphere which contains a high
concentration of ions and free electrons and is able to reflect radio
wave is known as
A. Ionosphere
B. Stratosphere
C. Mesosphere
D. Exosphere
Solution: Option A. Ionosphere, The layer of the earth’s atmosphere
which contains a high concentration of ions and free electrons and is
able to reflect radio wave is known as the ionosphere.
Question 2: In the following circuit, the battery E1 has an emf of 12V
and zero internal resistance while the battery E has emf of 2V If the
galvanometer G reads zero, then the value of the resistance X in ohm
is
a. 10
b. 100
c. 500
d. 200
Solution: Option B. I1=12/(500+x), I2=2/x. As the galvanometer has
zero deflection we have 12/(500+x)=2/x or x=100 ohms.
3. The normal movement of electric charges among the Earth’s
surface, the various layers of the atmosphere, and especially the
ionosphere, taken together, are known as :
A. a current conducting circuit
B. the global atmospheric electrical circuit
C. charge cloud
D. none of the above
Solution: Option C. The global atmospheric electrical circuit.
Wheatstone Bridge, Meter Bridge and Potentiometer
Every other day, science presents us with one or more ways to feel
amazed. There are a host of experiments that show both how we can
use things and make newer things out of them. Experiments related to
Wheatstone Bridge and the potentiometer are among few such things
in science that invoke a curious sense of amazement. Let us study
more about the concept of Wheatstone bridge and meter bridge, along
with potentiometer.
The Concept of Wheatstone Bridge
Defined simply, a Wheatstone Bridge is an electric circuit that is used
to measure the electrical resistance of a circuit. The circuit is set out
by balancing two legs of a bridge circuit. Out of the two, one of the
legs is an unknown component which was invented by Samuel Hunter
Christie in the year 1833 and later, it improved and popularized by Sir
Charles Wheatstone in the year 1843.
Nowadays, technological progress has allowed us to make various
measurements through sophisticated tools and machines. However,
even today, the wheat bridge remains an authentic way to measure
electric resistance, down to the closest milliohms as well.
The Principle behind the Wheatstone Bridge
The usual arrangement of the Wheat stone bridge circuit has four
arms. The bridge circuit where the arms are situated consist of
electrical resistance. Out of these resistances, P and Q are the fixed
electrical resistances and these two arms are the ratio arms. Next, A
Galvanometer connects between the terminals B and D through a
switch K2. The source of voltage of this arrangement is connected to
the terminals A and C through a switch, K1.
A variable resistor S is connected between point C and D. The
potential at point D is altered by adjusting the value of a variable
resistor. If a variation in the electrical resistance value of arm CD is
brought, the value of current I2 will also vary as the voltage across
both A and C is fixed.
If we continue to adjust the variable resistance, a situation may come
when the voltage drops across the resistor S that is I2. Here, S
becomes exactly equal to the voltage drop across resistor Q that is I1.
Q. So, the potential at point B becomes equal to the potential at point
D hence the potential difference between these two points is zero
hence current through galvanometer is nil. The deflection in the
galvanometer is nil when the switch K2 is closed.
Applying Kirchoff’Law, in this condition,
P/Q = R/S
How is the Meter Bridge experiment carried out using the Wheatstone Principle?
The meter bridge experiment uses the wheat bridge experiment to
demonstrate the resistance of an unknown conductor or to make a
comparison between two unknown resistors. Through the above-stated
equation, one can easily decipher the specific resistance of a given
material
Conclusions of the wheat stone bridge principle are:
According to the Wheatstone-bridge principle, the resistance of length
AB/resistance of length BC = R / X
Let l be the length of wire between A and B and then (100 – l) is the
length of wire between B and C. Here, P = ρl / A. Since the wire has a
uniform cross-section and ρ is constant. Its resistance is proportional
to the length. That is P ∝ l, and Q ∝ (100–l). So,
L / (100–l) = R / X
This is how to draw the values of X for different values of R and the
mean value gives the value of unknown resistance X.
The Concept of Potentiometer
A potentiometer is an electric device which is used to regulate EMF
and internal resistance of a given cell. This helps in providing a
variable resistance and therefore, a variable potential difference
arising between two points in an electric circuit. It is basically a
three-terminal resistor device with an adjustable arm that increases or
reduces the resistance in the loop.
Potentiometer (Source: Wikipedia)
Solved Examples for You
Question: Describe how a potentiometer works in an arrangement.
Answer: A potentiometer consists of a uniform wire AB of manganin
or constantan that has a length of usually 10 m. it is kept stretched
between copper stripes that are fixed on a wooden board by the side of
a metre scale. The wire is then divided into ten segments each of 1 m
length.
These segments join in series through metal strips between points A
and B. A steady current is maintained in the wire AB by a constant
source of EMF Eo, called driver cell, that connects between A and B
through a rheostat. A jockey slides over the potentiometer wire which
makes contact with the wire and cell.
Potentiometer (Source: Wikimedia)
Thus we can say that the potential difference across any portion of the
potential of the potentiometer wire is directly proportional to the
length of that portion provided the current is uniform.
Cells, EMF and Internal Resistance
Cells, EMF, Internal Resistance are the components which complete
the circuit and help the flow of electricity within the circuit. Cells, emf
and internal resistance are inter-related to one another. Batteries i.e.
Cells are posses internal resistance and potential difference i.e.
voltage. Know more about Cells, emf and internal resistance in this
article, explore more below!
Cells
An “electric power supply” is also an Electric cell. Cells generate
electricity and also derives chemical reactions. One or more
electrochemical cells are batteries. Every cell has two terminals
namely:
● Anode: Anode is the terminal from where the current flows in
from out i.e. it provides an incoming channel for the current to
enter the circuit or the device.
● Cathode: Cathode is the terminal from where the current flows
out i.e. it provides an outgoing current flow from the circuit or
the device.
There are different types of cells available and some of them are as
follows:
● Electric Cells
● Fuel Cells
● Secondary Cells
● Galvanic Cells
● Photovoilatatie Cells
● Solar Cells
● Storage Cells
● Primary Cells
[Source: Studytronics]
EMF
EMF is Electromotive Force, which is measured in coulombs of
charge. It is pressure developed or an electric intensity from a
electrical energy or a source. It is a device which converts any form of
energy into electrical energy which is then measured with coulombs of
charge. EMF i.e ElectroMotive Force id denoted by, .
emf = I (R + r)
Where I is the current in amperes; R is the resistance of load in the
circuit in ohms; r is the internal resistance in ohms.
emf = E/ Q
Where E is the energy in joules; Q is the charge in coulombs.
[Source: Energy Education]
Internal Resistance
When there is current present in the device or the electrical circuit and
there’s a voltage drop in source voltage or source battery is internal
resistance. It is caused due to electrolytic material in batteries or other
voltage sources.
Internal Resistance (r) = (E – V)/I
Where E is the emf of the device; V is the potential difference
between the device; I is the current in the device. Internal Resistance
is the result of the resistance in the battery or the accumulation in the
battery. the equation used to derive this is as follows:
V = (E – Ir)
[Source: Wikipedia]
Solved Examples for You
Question 1: The terminal voltage of a cell in an open circuit condition
is
A. Less than its emf
B. More than its emf
C. Equal to its emf
D. Depends on its internal resistance
Solution: Option C. Equal to its emf. The terminal voltage of a cell in
open circuit condition will be equal to the emf of the cell as the circuit
is open there won’t be any drop across the internal resistance.
Question 2: What is the p.d. across the terminals (VT) of a cell with
emf E for the open circuit?
A. VT<E
B. VT>E
C. VT=0
D. VT=E
Solution: Option D. VT=E, When the circuit is closed, the resulting
current not only flows through the external circuit but through the
source (battery, generator, transformer, etc.) itself. All sources have an
internal resistance, which causes an internal voltage drop, slightly
reducing the voltage across the terminals.
The larger the current, the larger the internal voltage drop, and the
lower the terminal voltage. When the circuit is open, no current flows.
So there is no internal voltage drop, and the full voltage appears across
the source’s terminals. This is why the potential difference across the
terminals of a cell when connected to a circuit is slightly lesser than
the emf of the cell.
Question 3: The common dry cell produces a voltage of:
A. 1.5V.
B. 30V.
C. 60V.
D. 3V
Solution: Option A. 1.5V, A common dry cell is a type of
electricity-producing chemical cell, commonly used today for many
home and portable devices, often in form of batteries. By standards, a
common dry cell has a constant voltage of 1.5
Cells in Series and Parallel
As we know the most frequently used method to connect electrical
components is Series Connection and Parallel Connection. Since the
cell is an important part of an electric circuit. To know more about
Cells, Series Connection and parallel Connection explore the article!
Cells
Cells generate electricity and also derives chemical reactions. One or
more electrochemical cells are batteries. Every cell has two terminals
namely:
1. Anode: Anode is the terminal from where the current flows in
from out i.e. it provides an incoming channel for the current to
enter the circuit or the device.
2. Cathode: Cathode is the terminal from where the current flows
out i.e. it provides an outgoing current flow from the circuit or
the device.
Learn more about Electric Charge here in detail
There are two simplest ways for cell connectivity are as follows:
1. Series Connection: Series connection is the connectivity of the
components in a sequential array of components.
2. Parallel Connection: Parallel connection is the connectivity of
the components alongside to other components.
Cells in Series Connection
In series, cells are joined end to end so that the same current flows
through each cell. In case if the cells are connected in series the emf
of the battery is connected to the sum of the emf of the individual
cells. Suppose we have multiple cells and they are arranged in such a
way that the positive terminal of one cell is connected to the negative
terminal of the another and then again the negative terminal is
connected to the positive terminal and so on, then we can that the cell
is connected in series.
Equivalent EMF/Resistance of Cells in Series
If E is the overall emf of the battery combined with n number cells
and E1, E2, E3 , En are the emfs of individual cells.
Then E1 + E2 + E3 + …….En
Similarly, if r1, r2, r3, rn are the internal resistances of individual cells,
then the internal resistance of the battery will be equal to the sum of
the internal resistance of the individual cells i.e.
r = r1 + r2+ r3 + rn
Cells in Parallel Connection
Cells are in parallel combination if the current is divided among
various cells. In a parallel combination, all the positive terminal are
connected together and all the negative terminal are connected
together.
Equivalent EMF/Resistance of Cells in Parallel
If emf of each cell is identical, then the emf of the battery combined
with n numbers of cells connected in parallel is equal to the emf of
each cell. The resultant internal resistance of the combination is,
r =
(
1
r
1
+
1
r
2
+
1
r
3
+……..
1
r
n
)-1
Equivalent EMF/Resistance of Cells in Series and Parallel
Assume the emf of each cell is E and internal resistance of each cell is
r. As n numbers of cells are connected in each series, the emf of each
series, as well as the battery, will be nE. The equivalent resistance of
the series is nr. As, m the number of series connected in parallel
equivalent internal resistance of that series and parallel battery is nr/m.
Solved Questions For You
Q. The internal resistance of a cell of emf 1.5 V, if it can deliver a
maximum current of 3 A is,
A. 0.5 Ω
B. 4.5 Ω
C. 2 Ω
D. 1 Ω
Solution: A. For maximum amount, load resistance = 0
⇒ E = Ir
r =
E
I
=
1.5
3
= 0.5 Ω
Q.2 For a given cell, its terminal voltage depends on
A. External resistance, Internal Resistance
B. External resistance
C. Internal Resistance
D. None of these
Solution: A. Inside the cell, the energy is put into the circuit by the
cell, but some of this energy is out by the internal resistor. So the
potential difference available to the rest of the circuit is the emf minus
the potential difference lost inside the cell.