ND
R
EVIEW


Battery: A battery is a device that has two terminals, one a + terminal and the other a - terminal,
and it maintains a constant potential difference (voltage) between these two terminals. The +
terminal is at a higher electric potential compared to the - terminal. During use, and when the
battery is not being charged, electrons exit the battery through the - terminal and enter through
the + terminal. Equivalently, we say that there is a

conventional electric current or just

electric current
from the positive terminal to the negative terminal in the exterior of the battery
during use.

Resistor: A conductor that offers resistance to the flow of charges. The only conductors that
offer no resistance to charge flow are superconductors. A resistor is represented by this symbol:




Battery Internal Resistance: A battery has a rated Maximum Electrical Potential also called the
electromagnetic force (emf) and one would be tempted to use this maximum electrical potential
as is when computing currents and electrical potential differences in a circuit. However the
battery also has an internal resistance due to the chemical processes within the battery. In a
generator the situation is similar and wires and other components create the internal resistance.
The internal resistance of the battery is an integral part of a circuit and has a measurable impact
on most circuits. The internal resistance can be modeled as a resistance in series with the other
elements of the circuit. And the total resistance of the circuit R
total
= R
load
+ r
internal
. So applying
Ohm's Law to the diagram below gives emf = i(R
load
+ r
internal
). As a result of the contribution of
the internal resistance the potential difference between the terminals of the battery will be
somewhat less than the maximum value indicated by the emf. Therefore the potential difference
between the terminals or the terminal voltage is equal to:
U = emf - ir
internal







R 2 / 6






1. A battery has an emf of 1.48 V and an internal resistance of 1.11
. What is the terminal
voltage of the battery when it is connected to a load resistance of 25.00
?





2. We will know consider the measurement of the terminal voltage of a battery using a voltmeter.
The probes of a voltmeter are placed on the terminals of a battery resulting in the circuit
presented below. The voltmeter contributes its own resistance to the circuit. You are measuring
the terminal voltage of a battery that has an emf of 1.35 V and an internal resistance of 2,000
.
The voltmeter has an input impedance of 10,000
. Compute the terminal voltage measured by
this voltmeter.



























Electrical circuit
including both an external
resistance R and the
internal resistance r of the
battery
Negative terminal
of the battery
Positive terminal
of the battery
r
Electrical circuit
including the internal
resistance r of the battery
and the resistance of the
voltmeter
Negative terminal
of the battery
Positive terminal
of the battery
r
R
Voltmeter
3 / 6

3. What will be the terminal voltage of the battery in question 2 if measured with a voltmeter
with an input impedance of 10 M
?







4. What determines whether or not the terminal voltage measured by a voltmeter is a good
approximation to the emf of the battery?







5. The circuit below is composed of two batteries and 3 resistors wired in parallel and in series.
Using the emf of the batteries (ignore the internal resistance of the batteries for the prelab)
compute currents in each part of the circuit. Use the junction rule and the loop rule to generate
as many equations as there are unknowns in the circuit and solve the resulting system of 3
equations with 3 unknowns. Once you have computed the currents, compute the voltage
differences across the different parts of the circuit. If you are not sure how to approach this
problem, read first in the course book the section on Kirchhoffs rules.























100

A
B
50

C
D
200

9 V
6 V
E 4 / 6




Currents Computed
Voltage
Computed
I
AB


V
AB


I
BC


V
BC


I
CD


V
CD


I
BE


V
BE


I
DA


V
DA








5 / 6
Y
OUR
N
AME
:
____________________ Date___________________
Group
Member
Names


1)___________________ 2) ___________________ 3) __________________


Physics 1402-Lab: Kirchhoffs Rules



At the beginning of the laboratory gather the following equipment for your group: a 6 Volt and a
9 Volt battery, a 100
, a 50 , and a 200 resistor.

Case1: Assemble a circuit as diagrammed below using the following Resistors: R
1
= 100
, R
2

= 50
, R
3
= 200
. Measure the terminal voltage of each battery. Use the measured terminal
voltages of the batteries and apply Kirchhoffs rule to compute the current and voltages in the
circuit. Finally check your computations by measuring the actual currents and voltages in the
circuit.






















Currents Computed Measured Voltage Computed Measured
I
AB



V
AB



I
BC



V
BC



I
CD



V
CD



I
BE



V
BE



I
DA



V
DA



R
1

A
B
R
3
R
2
C
D
9 V
Battery
6 V
Battery
E 6 / 6
Case2: Modify the circuit assembled in Case 1 following the circuit diagram below. The
resistors values are the following: R
1
= 100
, R
2
= 50
, R
3
= 200
. Measure the terminal
voltage of each battery. Use the measured terminal voltages of the batteries and apply
Kirchhoffs rule to compute the current and voltages in the circuit. Finally check your
computations by measuring the actual currents and voltages in the circuit.






















Currents Computed Measured Voltage Computed Measured
I
AB



V
AB



I
BC



V
BC



I
CD



V
CD



I
BE



V
BE



I
DA



V
DA






R
1

A
B
R
3

R
2
C
D
9 V
Battery
6 V
Battery
E