Resistance – Learning Outcomeslawlessteaching.eu/colaistebride/physics-6/current...
Transcript of Resistance – Learning Outcomeslawlessteaching.eu/colaistebride/physics-6/current...
Resistance – Learning Outcomes Define resistance and give its unit.
Solve problems about resistance.
State Ohm’s Law.
HL: Derive the formulas for resistors in series and parallel.
Solve problems about resistors in series and parallel.
Give the factors that affect the resistance of a
conductor.
Use an ohmmeter.
Solve problems about resistivity.
Resistance – Learning Outcomes Discuss light-dependent resistors (LDRs) and thermistors.
Demonstrate LDRs and thermistors.
HL: Describe wheatstone bridges.
HL: Solve problems about wheatstone bridges.
HL: Discuss uses of a wheatstone bridges.
HL: Use a metre bridge.
Resistance The resistance of a conductor is the ratio of the voltage
across it to the current flowing through it.
Formula: 𝑅 =𝑉
𝐼
Resistance is a scalar quantity measured in ohms (Ω).
A conductor has a resistance of 1 ohm if the current
through it is 1 ampere when the voltage across it is 1 volt.
Resistance is measured using an ohmmeter or
multimeter set to measure resistance – alternatively
calculate it by measuring current and voltage, then
using the formula.
Resistance
Resistance e.g. Find the resistance of a conductor if it carries a
current of 4 A when the voltage across it is 20 V.
e.g. What potential difference will produce a current of
5 A in a 12 Ω resistor?
e.g. At a certain temperature, the current through a
conductor is 3 A when the voltage across it is 24 V. Find
the resistance of the conductor.
When the temperature of the conductor is raised, the
same voltage causes a current of 2 A to flow through it.
Find the increase in its resistance.
Ohm’s LawOhm’s Law states the current flowing through a
conductor is proportional to the voltage across it at
constant temperature.
Formula: 𝑉 ∝ 𝐼
Constant temperature is required since resistance varies
with temperature – more on this later.
Some conductors will also vary their resistance with
voltage.
For conductors which obey Ohm’s Law, the constant of
proportionality is resistance:
Formula: 𝑉 = 𝐼𝑅 (the same formula we covered earlier)
Types of Resistor
Resistors in Series For two or more resistors in series, their total resistance is
the sum of their resistances.
Formula: RTotal = 𝑅1 + 𝑅2 + 𝑅3 +⋯
Resistors in Series To prove: RT = 𝑅1 + 𝑅2 + 𝑅3
Let 𝑉1, 𝑉2, 𝑉3 be the voltages across each resistor.
Let 𝐼 be the current through each resistor.
By formula, 𝑉1 = 𝐼𝑅1, 𝑉2 = 𝐼𝑅2, 𝑉3 = 𝐼𝑅3
But VT = 𝑉1 + 𝑉2 + 𝑉3
⇒ 𝑉𝑇 = 𝐼𝑅1 + 𝐼𝑅2 + 𝐼𝑅3
⇒ 𝐼𝑅𝑇 = 𝐼𝑅1 + 𝐼𝑅2 + 𝐼𝑅3
⇒ 𝐼𝑅𝑇 = 𝐼(𝑅1 + 𝑅2 + 𝑅3)
⇒ 𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3
Resistors in Series e.g. Calculate the total resistance of the following
resistors:
Resistors in Parallel For two or more resistors in parallel, their total resistance
is given by:
Formula: 1
𝑅𝑇=
1
𝑅1+
1
𝑅2+
1
𝑅3+⋯
Resistors in Parallel
To prove: 1
𝑅𝑇=
1
𝑅1+
1
𝑅2+
1
𝑅3
Let V be the voltage across each resistor.
Let 𝐼1, 𝐼2, 𝐼3 be the current through each resistor.
By formula, 𝐼1 =𝑉
𝑅1, 𝐼2 =
𝑉
𝑅2, 𝐼3 =
𝑉
𝑅3
But V
RT= 𝐼 = 𝐼1 + 𝐼2 + 𝐼3
So 𝑉
𝑅𝑇=
𝑉
𝑅1+
𝑉
𝑅2+
𝑉
𝑅3
So 1
𝑅𝑇=
1
𝑅1+
1
𝑅2+
1
𝑅3
Resistors in Parallel e.g. Calculate the total resistance of the following
resistors:
Resistance in Circuits e.g. What is the total resistance in this circuit? What is the
potential difference across the 9Ω resistor?
Resistance in Circuits e.g. What is the total resistance of this circuit? What is
the current flowing through the 3Ω resistor?
Resistance in Circuits e.g. If the bulb has resistance 4Ω, what is the total
resistance of this circuit? What is the current flowing
through the bulb?
Resistance in Circuits e.g. What is the total resistance of the following resistors?
Factors Affecting Resistance – Temperature
We already know that the resistance of a conductor
depends on temperature.
Increased temperature has two effects:
Heat releases extra electrons from the atoms, decreasing
resistance.
Heat causes atoms to vibrate more, increasing resistance.
For metallic conductors, very few electrons are released,
so resistance increases with increasing temperature.
For insulators and semiconductors, lots of electrons are
released, so resistance decreases with increasing
temperature.
Factors Affecting Resistance The resistance of a conductor also depends on:
Length, 𝑙,
Cross-sectional area, 𝐴,
Resistivity of the material, 𝜌.
Factors Affecting Resistance - LengthConsider a cuboid resistor:
What is the effect on resistance if a second identical
resistor is added in series?
It doubles ⇒ 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∝ 𝑙𝑒𝑛𝑔𝑡ℎ
Factors – Cross-Sectional AreaWhat if the second resistor is instead added in parallel?
Using 1
𝑅𝑇=
1
𝑅1+
1
𝑅2,
⇒1
𝑅𝑇=
2
𝑅1
⇒ 𝑅𝑇 =1
2𝑅1
The same is true if the resistors
are in contact.
⇒ 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∝1
𝐴𝑟𝑒𝑎
Factors - Resistivity Different materials come with a natural level of
resistance – we normalise this using resistivity.
The resistivity of a material is the resistance of a 1𝑚 ×1𝑚 × 1𝑚 cube of the material.
The relationship is: r𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∝ 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦
Factors Affecting Resistance Putting each of these factors into a single formula, we
get:
Formula: 𝑅 =𝜌𝑙
𝐴
We also get a definition for resistivity from this:
Formula: 𝜌 =𝑅𝐴
𝑙
Factors Affecting Resistance e.g. A uniform wire of length 2 m has a resistance of 12Ω.
Find the resistance of a piece of identical wire of length
14 m.
e.g. What length of copper wire of cross-sectional area
2 mm2 is needed to make a resistor of resistance 10 Ω?
Resistivity of copper = 1.7 × 10−8 Ω𝑚.
e.g. A coil of copper wire 20 m long has uniform
composition and uniform cross-sectional area. The
diameter of the wire is 0.055 mm. Calculate the
resistance of the coil if 𝜌𝑐𝑜𝑝𝑝𝑒𝑟 = 1.7 × 10−8 Ω𝑚.
Light-Dependent Resistor A light-dependent resistor (LDR) is
a semiconductor that decreases
its resistance when light shines on it.
Light hitting the resistor releases
electrons from the molecules,
allowing them to conduct electricity.
Thermistor A thermistor is a semiconductor
designed to decrease its resistance
as its temperature increases.
The heat energy frees electrons
from the material, allowing them
to be used for conduction.
Wheatstone Bridge In a wheatstone bridge, four
resistors are arranged around a
galvanometer such that no current
flows through the galvanometer.
This happens when the ratio of the
resistors is given by:
𝑅1
𝑅2=
𝑅3
𝑅4
Wheatstone Bridge – Uses Usually, one resistor is variable and
set to monitor something, while
the galvanometer is replaced by
some circuit.
e.g. A thermistor can be used to
monitor room / oven temperature
and the galvanometer can be
replaced by a heater.
When the thermistor unbalances
the circuit due to falling
temperature, a current flows and
activates the heater.
Also used in fail-safe devices.
Wheatstone Bridge e.g. If the bridge pictured is balanced, what is the value
of R?
Metre Bridge A metre bridge replaces one
side of a wheatstone bridge
with a resistive wire.
The galvanometer
connection can be made
anywhere on the wire and a
balance point will exist where:
𝑅1
𝑅2=
𝑙1
𝑙2
Usually one resistor is unknown
and this formula can be used
to find it.