question_answer

A 100 V voltmeter of internal resistance \[20\,k\Omega \] in series with a high resistance R is connected to a 110 V line. The voltmeter reads 5 V, the value of R is [MP PET 1999]

A)                    \[210\,k\Omega \]     

B)            \[315\,k\Omega \]

C)                    \[420\,k\Omega \]     

D)            \[440\,k\Omega \]

Correct Answer: C

Solution :

             Here \[i=\frac{110}{20\times {{10}^{3}}+R}\]                    \[\because \] \[V=iR\] Þ \[5=\left( \frac{110}{20\times {{10}^{3}}+R} \right)\times 20\times {{10}^{3}}\]            Þ \[{{10}^{5}}+5R=22\times {{10}^{5}}\]Þ \[R=21\times \frac{{{10}^{5}}}{5}=420\,K\Omega \]