Circuits

1
Circuits
6th Edition Chapter 28

• Chapter 27

2
Pumping Charges
Emf device is a tool to maintain a potential
difference between two terminals The device is
said to provide an emf E (electromotive
force) Common examples (batteries, electric
generators, solar cell)
3
Work, Energy, and Emf
In any time interval dt, a charge dq passes
through any cross section of the circuit (e.g.
aa'). The same amount of charge must.
enter the emf device at its low-potential end and
leave at its high-potential end.
4
Work, Energy, and Emf
The device must do an amount of work dW on the
charged dq to force it to move in this way. The
emf can be defined accordingly to be
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Work, Energy, and Emf

• The SI units of emf
• Joule per coulomb Volt
• An ideal emf device ? no internal resistance
• A real emf device ? has some resistance to the
  movement of charges inside it

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Work, Energy, and Emf
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Single-Loop Circuit
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Single-Loop Circuit - Current
Energy Method
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Single-Loop Circuit - Current
Potential Method
LOOP RULE The algebraic sum of the changes in
potential encountered in a complete traversal of
any loop of a circuit must be zero.
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Single-Loop Circuit - Current
Potential Method
RESISTANCE RULE For a move through a resistance
in the direction of the current, the change in
the potential is iR in the opposite direction
its is iR
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Single-Loop Circuit - Current
Potential Method
EMF RULE For a move through an ideal emf device
in the direction of the emf arrow, the change in
potential is E in the opposite direction it is
- E
12
Checkpoint 1
(a)What direction is the emf? At a, b and c rank
(b) the current, (c) the electric potential (d)
the electric potential energy of the charge
carrier, greatest first.
13
Single-Loop Circuit - Current
Internal Resistance
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Single-Loop Circuit - Current
Internal Resistance
15
Resistance in Series
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Checkpoint 2
If R1 gt R2 gt R3, rank the three resistors
according to (a) the current through (b) the
potential difference across them, greatest firs.
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Potential Differences
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Power, Potential, and Emf
Rate of energy transferred to the charge carrier.
Rate of energy transferred to thermal energy
within the device
Rate of energy transferred both the charge
carriers and to internal thermal energy.
19
Sample Problem 1

• In the circuit E14.4 V, E22.1 V, r12.3 O,
  r21.8 O, R5.5 O.
• What is the current i in the circuit?
• What is the potential difference between the
  terminal s of battery 1 in the figure?

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Sample Problem 1
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Checkpoint 3
A battery has an emf of 12 V and an internal
resistance of 2 O. Is the terminal-to-terminal
potential difference greater than, less that, or
equal to 12 V if the current in the battery is
(a) from the negative to the positive terminal,
(b) from the positive terminal to the negative
terminal and (c) zero?
22
Multiloop Circuits
JUNCTION RULE The sum of the currents entering
any junction must be equal to the sum of the
currents leaving that junction.
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Resistance in Parallel
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Checkpoint 4
A battery, with potential V across it and current
i through it, is connected to a combination of
two identical resistors. What are the potential
difference across and the current through either
resistor if the resistors are (a) in series and
(b) in parallel?
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Sample Problem 2

• In the circuit E12 V, R120 O, R220 O, R330 O
  , R48 O.
• What is the current through the battery?
• What is the current i2 through R2?
• What is the current i3 through R3?

26
The Ammeter and the Voltmeter
27
RC Circuits
RC circuits are circuits with capacitors and
resistors (beside batteries too!). Current in RC
circuits varies in time
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RC Circuits
Charging a Capacitor
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RC Circuits
Charging a Capacitor
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RC Circuits
Charging a Capacitor
31
RC Circuits
Charging a Capacitor Current
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RC Circuits
Charging a Capacitor Current
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RC Circuits
Charging a Capacitor Potential Difference
across the capacitor
34
RC Circuits
Time Constant (t)
At one time constant
35
RC Circuits
Discharging a Capacitor
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Sample Problem 5

• A capacitor of capacitance C is discharging
  through a resistor of resistance R.
• In terms of the time constant tRC, when will the
  charge on the capacitor be half its initial
  value?
• When will the energy stored in the capacitor be
  half its initial value?

37
Checkpoint 5
Rank the sets in the table according to (a) the
initial current (as the switch is closed on a)
and (b) the time required for the current to
decrease to half its initial value, greatest
first.
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Checkpoint 5
Rank the sets in the table according to (a) the
initial current (as the switch is closed on a)
and (b) the time required for the current to
decrease to half its initial value, greatest
first.
39
Problem Set 6 Q1

• Compute the equivalent resistance of the network
  in the figure, and find the current in each
  resistor. The battery has negligible internal
  resistance.

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Problem Set 6 Q2

• In the circuit shown , the voltage across the
  2.00 O resistor is 12.0 V. What are the emf of
  the battery and the current through the 6.00
  resistor?

41
Problem Set 6 Q3

• Find the emfs E1 and E2 in the circuit shown,
  and find the potential difference of point b
  relative to point a.

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Problem Set 6 Q4

• Find the current in each branch of the circuit
  shown and the potential difference between point
  a relative to b.

43
Problem Set 6 Q5

• A capacitor with capacitance C 455 pF is
  charged, with charge of magnitude 65.5 nC on each
  plate. The capacitor is then connected to a
  voltmeter that has internal resistance 1.28 M O.
  (a) What is the current through the voltmeter
  just after the connection is made? (b) What is
  the time constant if this RC circuit?

44
Problem Set 6 Q6

• How many 90-W, 120-V light bulb can be connected
  to a 20-A, 120-V circuit without tripping the
  circuit breaker?