Question

As a cell age, its internal resistance increases. A voltmeter of resistance 270 Ω connected across an old dry cell reads 1.44 V. However, a potentiometer at the balance point gives a voltage measurement of the cell as 1.5 V. Internal resistance of the cell is ______ Ω.

Options

• 11.11

• 11.25

• 12.23

• 14.45

Answer 1

As a cell age, its internal resistance increases. A voltmeter of resistance 270 Ω connected across an old dry cell reads 1.44 V. However, a potentiometer at the balance point gives a voltage measurement of the cell as 1.5 V. Internal resistance of the cell is 11.25 Ω.

Explanation:

The emf is the voltage measured by a potentiometer at the balance point. This is due to the fact that the current drawn from the cell at the balance point is zero.

Hence E = 1.5 V

If a voltmeter of resistance 270Ω is connected across the cell as shown,

I = `1.5/(270 + r)`

and voltage measured by the voltmeter.

V = IR_V (also V = E - Ir = 1.5 - Ir)

or V = `(1.5/(270 + r))270`

but V = 1.44 V (given)

∴ `(1.5/(270 + r))270 = 1.44`

or = 11.25 Ω