Question

A micro meter has a resistance of $100\Omega$ and a full scale of range of $50\mu \text{A}$. 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 combinations(s).

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

Answer 1

Answer: (B), (C)

The correct options are
B $10\text{V}$ range with $200\text{k}\Omega$ resistance in series
C $5\text{mA}$ range with $1\Omega$ resistance in parallel


To convert a galvanometer into a voltmeter of certain range say $V$, a high resistance $R$ is connected in series with the galvanometer so that current passing through the galvanometer of resistance $G$ becomes equal to its full scale deflection value $I_g$.

This is possible only if,

$V=I_g(G+R)i.e.,R=\frac{V}{I_g}-G$

For $V=10\text{V}$, $I_g=50\mu \text{A}$ , $G=100\Omega$

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

$R\approx 200\text{k}\Omega$

Hence, (b) option is the correct answer.


To convert a galvanometer into an ammeter of a certain range say $I$, a small resistance $S$ (called shunt) is connected in a parallel with the galvanometer so that the current passing through the galvanometer of resistance $G$ becomes equal to its full scale deflection value $I_g$.

This is possible only if,

$I_{g}G=(I-I_g)S$

$\therefore S=\frac{I_g}{(I-I_g)}G$

For , $I_g=50\mu \text{A}$ , $G=100\Omega$ and $I=5\text{mA}$

$S=\frac{50\times {10}^{-6}}{(5\times {10}^{-3}-0.050\times {10}^{-3})}\times 100$

$\therefore S\approx 1\Omega$

Hence option (c) is also correct.

Why this question ? Key concept : To convert a galvanometer into a voltmeter of certain range say $V$, a high resistance $R$ is connected in series with the galvanometer. To convert a galvanometer into an ammeter, a small resistance S (called shunt) is connected in parallel with the galvanometer

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