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CH 20-2
Model of a real battery
A real battery can be modeled as an ideal battery
(i.e. voltage source) and an internal resistance r.
The voltage across the terminals is
V =  - Ir
With usage, the internal resistance increases and
the voltage across the terminals decreases.
Example
The voltage across a battery is 1.5 V when it is not in a
circuit. When connected to a bulb, 0.5 A flows through
the battery, and the voltage across the terminals is 1.4
V. What is the internal resistance of the battery?
Ideal Voltage Source
We will treat all batteries as ideal voltage sources.
The voltage across its terminals is constant (and
therefore does NOT depend on the current through
the voltage source). The current through the voltage
source can have any value.
Series
When elements are connected in series, one element
is connected to another element in such a way that
there is only one path for current to flow through the
elements. The current through each element is the
same.
I
I
Total Resistance
For two resistors in series, the total resistance is the
sum of the resistances.
R1
R2
Req
Example
A 1.5 V battery is connected to a 6  resistor and a 10
 resistor that are in series. What is the current through
the battery?
R1
R2
Example
A 1.5 V battery is connected to a 6  resistor and a 10 
resistor that are in series. What is the voltage across
each resistor?
R1
R2
Voltage Divider
R1
R2
Adapted from
David Marx
Consider the three resistors and the battery in the circuit
shown. Which resistors, if any, are connected in series?
A. R1 and R2
B. R1 and R3
C. R2 and R3
D. R1 and R2 and R3
E. No resistors are connected in series.
In the circuit shown here,
elements _________ are in
series.
A. E2 and E5
E1
E3
B. E3 and E4
C. E4 and E5
D. none of the above
E2
E5
E4
In the circuit shown here,
the current will always be
equal through elements
_________.
A. E1 and E3
B. E2 and E5
C. E3 and E4
D. E4 and E5
E. none of the above
E1
E3
E2
E5
E4
R1
R2
R3
a•
•b
READING
QUESTION
In the arrangement shown, the resistances R1, R2, and R3
are all different. Here are four proposed statements about
this arrangement:
1. The current through each individual resistor is equal to the
current through point b.
2. The currents through all the individual resistors add up to the
current through point b.
3. The voltage across each individual resistor is equal to the
voltage between points a and b.
4. The voltages across all the individual resistors add up to the
voltage between points a and b.
Which of these statements are correct?
A. 1 and 3
B. 1 and 4
C. 2 and 3
D. 2 and 4
Parallel
Two elements are connected in parallel if their terminals
are connected to each other (on both sides). A voltmeter
across each element will read the same voltage.
Total Resistance
For two resistors in parallel, the total resistance is
LESS than the sum of the resistances.
R1
Req
R2
Example
A 1.5 V battery is connected to 6  and 10  resistors
that are in parallel. What is the current through the
battery?
R1
R2
Example
A 1.5 V battery is connected to 6  and 10  resistors
that are in parallel. What is the current through each
resistor?
R1
R2
Current Divider
R1
R2
Adapted from
David Marx
Consider the three resistors and the battery in the circuit
shown. Which resistors, if any, are connected in
parallel?
A. R1 and R2
B. R1 and R3
C. R2 and R3
D. R1 and R2 and R3
E. No resistors are connected in parallel.
In the circuit shown here,
elements _________ are in
parallel.
A. E2 and E3
B. E1 and E3
C. E3 and E5
E1
E3
E4
E2
E5
D. E1, E3, and E5
E. none of the above
Assume the connecting wires
have negligible resistance.
In the circuit shown here,
elements _________ are in
parallel.
A. E2 and E3
E1
E4
E3
B. E1 and E3
C. E3 and E5
D. E1, E3, and E5
E. none of the above
E2
E5
a•
R1
R2
R3
•b
READING
QUESTION
In the arrangement shown, the resistances R1, R2, and R3
are all different. Here are four proposed statements about
this arrangement:
1. The current through each individual resistor is equal to the
current through point b.
2. The currents through all the individual resistors add up to the
current through point b.
3. The voltage across each individual resistor is equal to the
voltage between points a and b.
4. The voltages across all the individual resistors add up to the
voltage between points a and b.
Which of these statements are correct?
A. 1 and 3
B. 1 and 4
C. 2 and 3
D. 2 and 4
R

RA1 
= 50
0.75
a
RR
309.0

B2=
b
 15
R3RC=3.0
6.0 V
In the above circuit, Which of the following correctly compares
the currents IA, IB, and IC passing through the three resistors?
A. IA > IB > IC
B. IC > IB > IA
C. IA > IC > IB
D. None of the above
Power
Power is change in energy per second (1 J/s = 1 W).
In the case of a battery, the power of the battery is
the rate that it supplies electrical energy. In the case
of a resistor, the power of the resistor is the rate that
it dissipates electrical energy (and converts it to
thermal energy and light energy).
The brightness of a light bulb depends on its power.
A “50 W” bulb and a “100 W” bulb are connected in
parallel with a standard 120 volt ac electrical outlet.
The brightness of a light bulb is directly related to
the power it dissipates. Therefore, the 100 W bulb
appears brighter. How does the brightness of the
two bulbs compare when these same bulbs are
connected in series with the same outlet?
A. Both bulbs will be equally bright.
B. The “100 W” bulb will be brighter.
C. The “50 W” bulb will be brighter.
Adapted from
David Marx