A galvanometer of internal resistance 100 ohms gives a full - scale deflection for a current of \(10 mA\). Determine the resistance necessary to convert the galvanometer to a voltmeter capable of reading up to 5V.
A. \(200 \Omega\) B. 400 \(\Omega\) C. \(300 \Omega\) D. \(0.1 \Omega\)
Correct Answer: B
Explanation
given: \(R_{g}=100 \Omega, I=10 mA , V=5 V , R_{m}=\) ? $$ V_{1}+V_{2}=V=5 V $$ $$ \begin{aligned} I R_{g}+I R_{m} &=V \\ I\left(R_{g}+R_{m}\right) &=V \\ R_{g}+R_{m} &=\frac{V}{I} \\ R_{m} &=\frac{V}{I}-R_{ g } \end{aligned} $$ $$ \begin{aligned} R_{m} &=\frac{5}{0.01}-100 \\ R_{m} &=500-100 \\ &=400 \Omega \end{aligned} $$
