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 $V=E-ir$
$=2\times \frac{1}{500}\times 2=2-\frac{1}{250}$
$\therefore Error=2-(2-\frac{1}{250})=\frac{1}{250}$
$=4\times 10^{-3}V$