Question

A microammeter has a resistance of $100\Omega$ and a full scale range of $50\mu A$. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combination(s)

• A. range 50 V, with a $10k\Omega$ resistance in series
• B. range 10 v, with a $(2\times {10}^5-100)\Omega$ resistance in series
• C. range 5 mA, with a $1.01\Omega$ resistance in parallel
• D. range 10 mA, with a $1\Omega$ resistance in parallel

Answer 1

Answer: (B), (C)

The correct options are
B range 10 v, with a $(2\times {10}^5-100)\Omega$ resistance in series
C range 5 mA, with a $1.01\Omega$ resistance in parallel

Given
$R_g=100\Omega$
$I_g=50\times {10}^{-6}A$
To use given galvanometer as an voltmeter a large resistance$R_v$ should be connect in series to it.
$\left(i\right)$ Consider, $V=50$ V,
$R_v=\frac{V}{I_g}-R_g$
$R_v=\frac{50}{50\times {10}^{-6}}-100$
$R_v=100000-100=99900\Omega$
$\left(ii\right)$ Consider, $V=10$ V,
$R_v=\frac{V}{I_g}-R_g$
$R_v=\frac{10}{50\times {10}^{-6}}-100$
$R_v=(0.2\times {10}^6-100)\Omega$
$R_v=(2\times {10}^5-100)\Omega$
To use given galvanometer as an ammeter a shunt resistance $S$ should be connect in parallel to it.
$\left(i\right)$ Consider, $I=5$ mA
$S=\frac{R_g{I}_g}{I-I_g}$
$S=\frac{100\times 50\times {10}^{-6}}{5\times {10}^{-3}-50\times {10}^{-6}}$
$S=\frac{5\times {10}^{-3}}{5\times {10}^{-3}-0.05\times {10}^{-3}}$
$S=\frac{5\times {10}^{-3}}{4.95\times {10}^{-3}}$
$S=1.01\Omega$
$\left(ii\right)$ Consider, $I=10$ mA
$S=\frac{R_g{I}_g}{I-I_g}$
$S=\frac{100\times 50\times {10}^{-6}}{10\times {10}^{-3}-50\times {10}^{-6}}$
$S=\frac{5\times {10}^{-3}}{10\times {10}^{-3}-0.05\times {10}^{-3}}$
$S=\frac{5\times {10}^{-3}}{9.95\times {10}^{-3}}$
$S=0.502\Omega$