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

• A

  $4\times {10}^{-1}\mathrm{ V}$
• B

  $2\times {10}^{-3}\mathrm{ V}$
• Correct answer
  C

  $4\times {10}^{-3}\mathrm{ V}$
• D

  $2\times {10}^{-1}\mathrm{ V}$

Solution

$I=\frac{2}{998+2}=\frac{2}{1000}=2\times {10}^{-3}\mathrm{A}$

$=2 \mathrm{m}\mathrm{A}$

Internal resistance is $2 \mathrm{\Omega }$

Hence, the measure of emf will be

$E=2-I\times 2$

$=2-2 \mathrm{m}\mathrm{A}\times 2$

Therefore, error in measured value $=4\times {10}^{-3}\mathrm{ V}$

Hence, the correct answer is option: 'C'.