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Internal Resistance
Thus far we have referred to a battery as a source of
voltage and we have made the assumption that the battery
_________
battery would be able to
is an ideal source. An ideal __________
maintain the same _______________
_____________
potential
difference
between its terminals regardless of the current drawn.
Consider the following diagram:
+
r
VT
ε
r
Internal resistance of
the real battery
ε emf of the battery
VT
Terminal voltage of the
battery (the actual voltage
applied to the external circuit)
Which value is larger ε or VT? Why
emf is larger because VT is the voltage put out by the
battery after some of the emf has been ‘lost’ to the internal
resistance
Derive an expression that relates ε and VT
(assume a current flows through the internal resistance)
ε = VT + Ir
Would the value of the resistance connected
across the terminals of the battery effect the
emf of the battery? Explain.
No; emf is determined by the electrochemical processes
within the battery
Would the value of the resistance connected
across the terminals of the battery effect the
terminal voltage of the battery? Explain.
Yes; the bigger the resistance across the terminals of the
battery, the smaller the current drawn and thus the bigger VT
Would the value of the resistance connected
across the terminals of the battery effect the
internal resistance of the battery? Explain.
No; internal resistance is determined by the makeup of the
components of the battery
Practice Exercise
Suppose a battery has an emf of 15.0 V. When a resistance of
2.0 ohms is placed across the battery terminals, 72 Watts is
dissipated in the 2 ohm resistor. Determine the internal
resistance of the battery.
Draw the circuit
ε = 15.0 V
Given:
Since 72 watts is
dissipated in the 2Ω
resistor, we can easily
determine the voltage
across this resistor
RL = 2Ω
PL = 72 watts
r
ε
2Ω
Find this value
Real battery
2
2
72 = V
V= 12 V
2
terminal _____________
voltage
This is also the __________
of the battery.
P= V
R
Use Ohm’s Law to determine the current through the circuit.
VT = IT RT
12 = I (2)
IT = 6 amps
This is also the current flowing through the __________
internal
resistance of the battery.
_____________
Now that we know the emf, current, and terminal voltage, we
can solve for the internal resistance of the battery.
ε = VT + Ir
15 = 12 + (6)r
r = 0.5Ω
Now solve for the power dissipated in the battery.
P = IV
P = (6)(3) = 18 watts
Current through
internal resistance.
Voltage across
internal resistance.