Question

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

• A. $50V$ range with $10k\Omega$ resistance in series
• B. $10V$ range with $200k\Omega$ resistance in series
• C. $5mA$ range with $1\Omega$ resistance in parallel
• D. $10mA$ range with $1k\Omega$ resistance in parallel

Answer 1

Answer: (B), (C)

$10V$ range with $200k\Omega$ resistance in series
$5mA$ range with $1\Omega$ resistance in parallel

Given

$R_g=100\Omega$

$I_g=50\times {10}^{-6}A$

To use given galvanometer as a voltmeter, a large resistance $R_v$should be connected in series to it.

$\left(i\right)$ Consider, V $=$ 50 V,

$R_v=\frac{V}{I_g}-R_g$
$R_v=\frac{50}{50\times {10}^{-6}}-100$

$R_v=100000-100=99900\Omega$

$R_v\approx 100K\Omega$

i.e. galvanometer can be converted to voltmeter of $50V$ range with

$100K\Omega$ resistance in series

$\left(ii\right)$ Consider, V $=$ 10 V,

$R_v=\frac{V}{I_g}-R_g$

$R_v=\frac{10}{50\times {10}^{-6}}-100$

$R_v=(0.2\times {10}^6-100)\Omega$

$R_v=(2\times {10}^5-100)\Omega$

$R_v\approx 2\times {10}^5\Omega$

i.e. galvanometer can be converted to voltmeter of $10V$ range

with $2\times {10}^5\Omega$ resistance in series

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

$S=\frac{R_g{I}_g}{I-I_g}$

$S=\frac{100\times 50\times {10}^{-6}}{5\times {10}^{-3}-50\times {10}^{-6}}$

$S=\frac{5\times {10}^{-3}}{5\times {10}^{-3}-0.05\times {10}^{-3}}$
$S=\frac{5\times {10}^{-3}}{4.95\times {10}^{-3}}$

$S=0.01\Omega \approx 1\Omega$

i.e. galvanometer can be converted to ammeter of $5mA$ range with $1\Omega$ resistance in parallel.

$\left(ii\right)$ Consider, $I=10$ mA

$S=\frac{R_g{I}_g}{I-I_g}$

$S=\frac{100\times 50\times {10}^{-6}}{10\times {10}^{-3}-50\times {10}^{-6}}$

$S=\frac{5\times {10}^{-3}}{10\times {10}^{-3}-0.05\times {10}^{-3}}$

$S=\frac{5\times {10}^{-3}}{9.95\times {10}^{-3}}$

$S=0.502\Omega \approx 0.5\Omega$

i.e. galvanometer can be converted to ammeter of $10mA$ range with $0.5\Omega$ resistance in parallel.