Question

A voltmeter having a resistance of $ 998 \Omega$ is connected to a cell of emf $2V$ and internal resistance $ 2 \Omega$ . 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)

Current taken form the cell
$ i = \frac{E}{R + r} $
Given, $ \, \, \, E = 2V, R = 998 \omega $ and $ r = 2\Omega$
$ \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 $