A galvanometer has a coil of resistance $100\Omega$ and gives a full scale deflection for $30 ext{ mA}$ curr

Question

A galvanometer has a coil of resistance $100\Omega$ and gives a full scale deflection for $30 	ext{ mA}$ current. If it is to work as a voltmeter of $30	ext{ V}$ range, the resistance required to be added will be

Accepted Answer

1. **Concept:** To convert a galvanometer into a voltmeter, a high resistance ($R$) is connected in series with the galvanometer coil. This ensures that the total resistance is high enough to draw negligible current from the circuit being measured.
2. **Formula:** According to Ohm's Law, the voltage drop across the series combination must equal the desired range ($V$) when the full-scale deflection current ($I_g$) flows through it. The equation is:
   $$V = I_g (R_G + R)$$
   Where:
   - $V$ is the voltage range ($30 	ext{ V}$).
   - $I_g$ is the full-scale deflection current ($30 	ext{ mA} = 30 	imes 10^{-3} 	ext{ A}$).
   - $R_G$ is the galvanometer resistance ($100 \Omega$).
   - $R$ is the external resistance to be added .
3. **Calculation:** Rearranging the formula for $R$:
   $$R = \frac{V}{I_g} - R_G$$
   $$R = \frac{30}{30 	imes 10^{-3}} - 100$$
   $$R = \frac{1}{10^{-3}} - 100$$
   $$R = 1000 - 100 = 900 \Omega$$

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