Question

An $80\Omega$ galvanometer deflects full-scale for a potential of 20 mV. A voltmeter deflecting full-scale of 5 V is to be made using this galvanometer. We must connect

• A. a resistance of $19.92$ $\Omega$ parallel to the galvanometer
• B. a resistance of $19.92$ $\Omega$ in series with the galvometer
• C. a resistance of $20$ k$\Omega$ parallel to the galvanometer
• D. a resistance of $20$ k$\Omega$ in series with the galvanometer

Answer 1

The correct option is B a resistance of $19.92$ $\Omega$ in series with the galvometer

The current through the galvanometer producing full-scale deflection is
$I=\frac{V}{R}$
where, variables have their usual meanings
$I=\frac{20\times {10}^{-3}}{80}$
$\therefore I=2.5\times {10}^{-4}A$
To convert the galvanometer into a voltmeter, a high resistance is connected in series with the galvanometer.
Therefore,
$R=\frac{V}{I_G}-G$
$R=\frac{5}{2.5\times {10}^{-4}}-80$
$R=20000-80$
$R=19920$ $\Omega$
$R=19.92$ k$\Omega$