Chapter 28: DC and RC Circuitssrjcstaff.santarosa.edu/~lwillia2/42/42ch28.pdf · 2012. 10. 11. ·...
Transcript of Chapter 28: DC and RC Circuitssrjcstaff.santarosa.edu/~lwillia2/42/42ch28.pdf · 2012. 10. 11. ·...
Chapter 28:
DC and RC Circuits
Kirchhoff’s Rules
Limitations of DC Transmission
• Large currents in wires produce heat and energy losses by
P = I2R.
• Large expensive conductors would be needed or else very
high voltage drops (and efficiency losses) would result.
• High loads of direct current could rarely be transmitted for
distances greater than one mile without introducing
excessive voltage drops.
• Direct current can not easily be changed to higher or lower
voltages. Separate electrical lines are needed to distribute
power to appliances that used different voltages, for
example, lighting and electric motors.
Advantages of AC Transmission
• Alternating Current can be transformed to ‘step’ the
voltage up or down with transformers.
• Power is transmitted at great distances at HIGH voltages
and LOW currents and then stepped down to low voltages
for use in homes (240V) and industry (440V).
• Convert AC to DC with a rectifier in appliances.
AC is more efficient for Transmission
& Distribution of electrical power than
DC over long distances! But what if the
power generation is LOCAL?
In The Future…. Long Distance AC Power Transmission may
not be needed!!! New DC technologies and
Solar Power will make AC obsolete!
War of Currents 1880’s
Thomas Edison, American
inventor and businessman,
pushed for the development
of a DC power network.
George Westinghouse,
American entrepreneur
and engineer, backed
financially the
development of a
practical AC power
network.
Nikola Tesla,
Serbian inventor,
physicist, and
electro-mechanical
engineer, was
instrumental in
developing AC
networks.
The first electric chair, which was used to execute William Kemmler in 1890
Edison wired NYC with DC. He carried out a campaign to discourage the use of
AC, including spreading information on fatal AC accidents, killing animals, and
lobbying against the use of AC in state legislatures. Edison opposed capital
punishment, but his desire to disparage the system of alternating current led to the
invention of the electric chair. Harold P. Brown, who was at this time being secretly
paid by Edison, constructed the first electric chair for the state of New York in
order to promote the idea that alternating current was deadlier than DC.
Edison's Publicity Campaign
The first electric chair,
which was used to execute
William Kemmler in 1890
Nebraska: Only state that requires it.
15-second-long jolt of 2,450 volts of
electricity (~ 8 Amps)
GE & Edison: We bring good things to light.
More than a 1000 killed since 1890!
Any practical distribution system will use voltage levels quite sufficient for a dangerous amount of current to flow, whether it uses alternating or direct current. Ultimately, the advantages of AC power transmission outweighed this theoretical risk, and it was eventually adopted as the standard worldwide after Nikola Tesla designed the first AC hydroelectric power plant at Niagara Falls, New York which started producing electrical power in 1895.
Is AC Deadlier than DC?
They are BOTH Deadly!
Is AC Deadlier than DC?
• Low frequency (50 - 60 Hz) AC currents can be more dangerous than similar levels of DC current since the alternating fluctuations can cause the heart to lose coordination, inducing ventricular fibrillation, which then rapidly leads to death.
• High voltage DC power can be more dangerous than AC, however, since it tends to cause muscles to lock in position, stopping the victim from releasing the energized conductor once grasped.
• Frequency MATTERS.
Electric Shock
•Electric Shock occurs when current is
produced in the body, which is caused by an
impressed voltage.
•Voltage is the CAUSE
•Current does the DAMAGE
What causes electric Shock in the human
body, Voltage or Current?
Current (A) Effect
0.001 Can be felt
0.005 Painful
0.010 Causes involuntary muscle
spasms
0.015 Causes loss of muscle control
0.070 If through heart, serious!
If current lasts for 1 s - FATAL!
Dry Skin Body Resistance: 500,000
Wet Skin Body Resistance: 1000
Electric Shock
Question
What current would you draw if you
were unfortunate to short-circuit a
120 V line with dry hands?
Wet hands?
DRY: I = V/R = 120 V/500,000 = .00024 (live!)
WET: I = V/R = 120 V/1000 = .12 (dead!)
Dry Skin Body Resistance: 500,000
Wet Skin Body Resistance: 1000
Ground Wire
• Electrical equipment manufacturers use electrical cords that have a third wire, called a ground
• This safety ground normally carries no current and is both grounded and connected to the appliance
Ground-Fault Interrupters
(GFI)
• Special power outlets
• Used in hazardous areas
• Designed to protect people from electrical
shock
• Senses currents (< 5 mA) leaking to ground
• Quickly shuts off the current when above
this level
Electric Shock Therapy
ELECTRO CONVULSIVE
THERAPY
An electric shock is applied to produce a convulsive
seizure. The shock is typically between 140 - 170 volts and
lasts between 0.5 and 1 seconds. No explanation of how it
works.
Used in the treatment of:
1.Chronic endogenous depression
2.Bipolar disorder.
3.Acute mania.
4.Certain types of schizophrenia
In the U.S. 33,000 - 50,000 people receive ECT each year
• The current is the same in each device.
• The equivalent resistance of the circuit is the sum
of the individual resistances.
Series Circuits
• The voltage of each device is the full
voltage of the EMF source (the battery)
• The total current is divided between
each path:
Parallel Circuits
1 2
1 1 1
totalR R R
1 2totalR R R
Find Everything
1 2 215.0V, 10.0 , 20.0 , 30.0 ,V R R R
YOU DO IT.
For the circuit shown, find the equivalent resistance of the
circuit, the total current drawn by the battery, and the
current through and the potential difference across each
resistor. Place your results in a table for ease of reading.
Voltage in a single-resistor circuit
with an Ideal 1.5 Volt battery
• The emf e is the voltage labeled on the battery. It is greater than the terminal voltage. DV=IR
• The actual potential difference DV between the terminals of the battery depends on the current in the circuit and the internal resistance of the battery: DV = e – Ir
• If the internal resistance of the battery is zero, the terminal voltage equals the emf : DV = e
• R is the load resistance: DV = IR
Electromotive Force: EMF
e = DV+ Ir
Power
• The total power output of the battery is
• This power is delivered to the external resistor (I 2 R) and to the internal resistor (I2 r) is maximum when R = r!! (see nice proof in text)
I V Ie D
2 2I R I r
Single Circuit: Multiple Batts What is the direction of current?
Book: Chooses Wrong Current Directions to show you that the rule still
works, you get negative currents. But try to pick the correct direction!
The 12 V WINS!
When polarities of the batteries are opposed, one gets CHARGED.
I
Book
Kirchhoff’s Rules When resistors are connected so that the circuits
formed cannot be reduced to a single equivalent
resistor you can use two rules, called Kirchhoff’s
rules, to solve the problem by generating systems
of equations to find the unknowns!!
Gustav Kirchhoff • 1824 – 1887
• German physicist
• Worked with Robert
Bunsen
• They
– Invented the
spectroscope and
founded the science of
spectroscopy
– Discovered the elements
cesium and rubidium
– Invented astronomical
spectroscopy
Kirchhoff’s Rules for Spectra: 1859
Bunsen
German physicist who developed the spectroscope and the science of
emission spectroscopy with Bunsen.
Kirkoff
* Rule 1 : A hot and opaque solid, liquid or highly compressed gas emits a continuous spectrum.
* Rule 2 : A hot, transparent gas produces an emission spectrum with bright lines.
* Rule 3 : If a continuous spectrum passes through a gas at a lower temperature, the transparent
cooler gas generates dark absorption lines.
Kirchhoff’s Junction Rule
• Junction Rule
– The sum of the currents at any junction must
equal zero
• Currents directed into the junction are entered
into the -equation as +I and those leaving as -I
• A statement of Conservation of Charge
– Mathematically, 0
junction
I
More about the Junction Rule
• I1 - I2 - I3 = 0
• Required by
Conservation of
Charge
• Diagram (b) shows a
mechanical analog
What are the
magnitude and the
direction of the
current in the fifth
wire?
A. 15 A into the junction
B. 15 A out of the junction
C. 1 A into the junction
D. 1 A out of the junction
E. Not enough data to determine
A. 15 A into the junction
B. 15 A out of the junction
C. 1 A into the junction
D. 1 A out of the junction
E. Not enough data to determine
What are the
magnitude and the
direction of the
current in the fifth
wire?
Kirchhoff’s Loop Rule
• Loop Rule
– The sum of the potential differences across all
elements around any closed circuit loop must
be zero
• A statement of Conservation of Energy
• Mathematically,
closedloop
0VD
Using the Loop Rule • Traveling around the loop
from a to b
• In (a), the resistor is
traversed in the direction
of the current, the
potential across the
resistor is – IR
• In (b), the resistor is
traversed in the direction
opposite of the current, the
potential across the
resistor is is + IR
Loop Rule
• In (c), the source of emf is traversed in the direction of the emf (from – to +), and the change in the electric potential is +ε
• In (d), the source of emf is traversed in the direction opposite of the emf (from + to -), and the change in the electric potential is –ε
which means you are CHARGING the battery!
I
I
Discharging
Charging
Junction Equations
from Kirchhoff’s Rules
• Use the junction rule as often as needed, so
long as each time you write an equation,
you include in it a current that has not been
used in a previous junction rule equation
– In general, the number of times the junction
rule can be used is one fewer than the number
of junction points in the circuit
0junction
I
Loop Equations from
Kirchhoff’s Rules
• The loop rule can be used as often as
needed so long as a new circuit element
(resistor or battery) or a new current appears
in each new equation
• You need as many independent equations as
you have unknowns
closedloop
0VD
Kirchhoff’s Rules Equations
• In order to solve a particular circuit problem,
the number of independent equations you need
to obtain from the two rules equals the number
of unknown currents
• Any capacitor acts as an open branch in a
circuit
– The current in the branch containing the capacitor is
zero under steady-state conditions
• Junction Rule:
• Loop Rule:
Kirchhoff’s Rules
•First use junction rule and assign values to the current - guess the directions!
•Then use the loop rule CONSISTENTLY (e.g. Clockwise) on each loop.
•Any capacitor acts as an open branch in a circuit once under steady state conditions
0junction
I
closedloop
0VD
Multiple Loop Circuit
Find the Currents! Book: Chooses Wrong Current Directions to show you that the rule still
works, you get negative currents. But try to pick the correct direction!
I1 I2
I3 I3
I1
Kirchhoff Problem
Taking R = 1.00 kM and ε = 250V, determine
the direction and magnitude of the current in
the horizontal wire between a and e.
Many-Loop – Many Equations! You can solve systems of equations with simple algebra or
by using linear algebra (Cramer’s Rule) but I can’t teach
you that! I’ve put a document on the website if you want to
teach yourself. BUT YOU DON’T NEED TO! Algebra
will work and I won’t put a circuit with more than two
loops on the exam! Also, you calculator can solve systems
of equations!
RC Circuits: Charging The capacitor continues to charge until it reaches its maximum
charge (Q = Cε). Once the capacitor is fully charged, the current
in the circuit is zero and the The potential difference across the
capacitor matches that supplied by the battery.
RC Circuit: Charging
• The charge on the capacitor varies
with time
q(t) = Ce(1 – e-t/RC) = Q(1 – e-t/RC)
t is the time constant
• t = RC
• The current can be found
I( ) t RCεt e
R
• The time constant t has units of time represents the time required
for the charge to increase from zero to 63.2% of its maximum
• The energy stored in the charged capacitor is ½ Qe = ½ Ce2
Discharging a Capacitor in an RC
Circuit • When a charged capacitor is
placed in the circuit, it can be discharged – q = Qe-t/RC
• The charge decreases exponentiallyAt t = t = RC,
the charge decreases to 0.368 Qmax
– In other words, in one time constant, the capacitor loses 63.2% of its initial charge
• The current is:
I t RCdq Qt e
dt RC
I( ) t RCεt e
R
q(t) = Q(1 – e-t/RC)
Active Figure: RC Circuit Charging
An RC Problem
The switch in the figure has been in position a for a long time. It is
changed to position b at t = 0s. What are the charge on the capacitor
and the current I through the resistor
a)immediately after the switch is closed?
b)What is the time constant t ?
c)at t = 50 s?
d)at t = 200 s?
What is the current in the
resistors?
What is the emf and internal
resistance of the battery?