Download Chapter 28

Chapter 28
Direct Current Circuits
Dr. Jie Zou
PHY 1361
1
Outline



Electromotive force (28.1)
Resistors in series and parallel (28.2)
Examples
Dr. Jie Zou
PHY 1361
2
Electromotive force

A battery





An actual circuit
Dr. Jie Zou

provides a voltage (potential difference)
with a fixed polarity, resulting in a direct
current in a circuit.
is a source of energy for the circuit.
is called a source of electromotive force or
a source of emf.
Direct current: a current that is
constant in direction.
In general we assume that the
connecting wires have no resistance.
The emf  of a battery is the maximum
possible voltage that the battery can
provide between its terminals.
PHY 1361
3
Internal resistance of a
battery



A circuit diagram

Internal resistance r: The resistance to
the flow of charge within the battery.
Terminal voltage V: The potential
difference across the battery.
Load resistance R: The external
resistance.
Terminal voltage V =  - Ir.




Dr. Jie Zou
Open-circuit voltage: If I = 0, then V = .
Ideal battery: r = 0 and V = .
Current I = /(R + r).
Total power output of the battery I =
I2R + I2r.
PHY 1361
4
Examples

Example 28.1: A battery has an emf of
12.0 V and an internal resistance of
0.05 . Its terminals are connected to a
load resistance of 3.00 .



Dr. Jie Zou
(A) Find the current in the circuit and the
terminal voltage of the battery.
(B) Calculate the power delivered to the load
resistor, the power delivered to the internal
resistance of the battery, and the power
delivered by the battery.
Example 28.2 Matching the load: Show
that the maximum power delivered to
the load resistance R occurs when the
load resistance matches the internal
resistance (when R = r).
PHY 1361
5
Resistors in series

Properties of series combination:



I1 = I2 = I
V = V1 + V2
Req = R1 + R2 +… (Req is greater than any individual resistance.)
Dr. Jie Zou
PHY 1361
6
Resistors in parallel

Properties of parallel combination:



I = I1 + I2
V1 = V2 = V
1/Req = 1/R1 + 1/R2 +… (Req is less than the smallest
resistance in the group.)
Dr. Jie Zou
PHY 1361
7
Examples
(a)

(b)
Quick Quiz 28.4 and 28.7:


(a) What happens to the reading on the ammeter when the
switch is opened?
(b) What happens to the reading on the ammeter when the
switch is closed?
Dr. Jie Zou
PHY 1361
8
Example 28.4 Find the
equivalent resistance

Four resistors are connected as
shown.


Dr. Jie Zou
(A) Find the equivalent resistance
between points a and b.
(B) What is the current in each
resistor if a potential difference of
42 V is maintained between a and
c?
PHY 1361
9
Example 28.6 Three resistors
in parallel

Three resistors are connected in
parallel as shown. A potential
difference of 18.0 V is maintained
between points a and b.



Dr. Jie Zou
(A) Find the current in each resistor.
(B) Calculate the power delivered to
each resistor and the total power
delivered to the combination of
resistors.
(C) Calculate the equivalent resistance
of the circuit.
PHY 1361
10
Real world example: Operation of
a three-way light bulb
Dr. Jie Zou
PHY 1361
11