A-level Physics (Advancing Physics)/Internal Resistance

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Batteries, just like other components in an electric circuit, have a resistance. This resistance is known as internal resistance. This means that applying Ohm's law (V = IR) to circuits is more complex than simply feeding the correct values for V, I or R into the formula.

The existence of internal resistance is indicated by measuring the potential difference across a battery. This is always less than the EMF of the battery. This is because of the internal resistance of the battery. This idea gives us the following formula:

Internal resistance.svg

PD across battery = EMF of battery - voltage to be accounted for

Let us replace these values with letters to give the simpler formula:

Vexternal = E - Vinternal

Since V = IR:

Vexternal = E - IRinternal

You may also need to use the following formula to work out the external potential difference, if you are not given it:

Vexternal = IΣRexternal

You should also remember the effects of using resistors in both series and parallel circuits.

Questions[edit]

1. A 9V battery is short-circuited. The potential difference across the battery is found to be 8V, and the current is 5A. What is the internal resistance of the battery?

2. What is the EMF of the battery in the following circuit?

Internal resistance q2.svg

3. What is the internal resistance of the battery in the following circuit?

Internal resistance q3.svg

Worked Solutions