Internal resistance

Before the switch is turned on

• The battery does not supply current to the light bulb

• Voltmeter reading = E.m.f. of battery

After the switch is turned on

• The battery supplies current which flows around the circuit

• Voltmeter measures the potential difference across the terminals of the battery

• The voltmeter reading drops due to internal resistance of the battery

EMF = IR + Ir
EMF = V + Ir
EMF = I (R + r)

where EMF = electromotive force [V]
I = current flowing through the circuit [A]
R = total resistance of the circuit [Ω]
r = internal resistance of the batteries [Ω]
V = potential difference of the circuit [V]


Worked example:

What is the internal resistance of a battery if its emf is 12 V and the voltage drop across its terminals is 10 V when a current of 4 A flows in the circuit when it is connected across a load?

Solution:
E = V + Ir

12 = 10 + 4(r)

r =0.5Ω