Question

A high-resistance voltmeter measures the potential difference across a battery as 9 V. On connecting a 24 Ω resistor across the terminals of the battery, the reading of the voltmeter is 7.2 V. Calculate the internal resistance of the battery.

Answer 1

Given Data:

Electromotive force of the battery (E) = 9 V (Voltage measured across open circuit)

Terminal voltage (V) = 7.2 V (Voltage when load is connected)

External resistance (R) = 24 Ω

Let the internal resistance of the battery be r.

Using Ohm’s law for the external circuit:

I = `V/R`

= `7.2/24`

= 0.3 A

Using the terminal voltage relationship formula:

V = E − I × r

7.2 = 9 − (0.3 × r)

0.3 × r = 9 − 7.2

0.3 × r = 1.8

r = `1.8/0.3`

r = 6 Ω

The internal resistance of the battery is 6 Ω.