Question

A voltmeter having a resistance of $998 O$ is connected to a cell of emf 2 V and internal resistance $2 O$ . The error in the measurement of emf will be

• A. $4 \times 10^{-1} V$
• B. $2 \times 10^{-3} V$
• C. $4 \times 10^{-3} V$
• D. $2 \times 10^{-1} V$

Answer 1

Answer: (C)

$4 \times 10^{-3} V$

Answer 2

Current taken form the cell
$i = \frac{E}{R + r}$
Given, $\, \, \, E = 2V, R = 998 O$ and $r = 2O$
$\therefore \, \, \, i = \frac{2}{998 + 2} = \frac{1}{500} A$
Error in value of emf
= Actual value of emf - measured emf
Emf V = E - ir
$\, \, \, \, = 2 \times \frac{1}{500} \times 2 = 2 - \frac{1}{250}$
$\therefore Error = 2 - \bigg( 2 - \frac{1}{250} \bigg ) = \frac{1}{250}$
$= 4 \times 10^{-3} V$