The current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflect

Question

The current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is:

Accepted Answer

1. **Definitions:**
   - Current Sensitivity ($I_s$) is the deflection per unit current: $I_s = \frac{\phi}{I}$ .
   - Voltage Sensitivity ($V_s$) is the deflection per unit voltage: $V_s = \frac{\phi}{V}$ .
2. **Relationship:** According to Ohm's Law, $V = IR$, where $R$ is the resistance of the galvanometer.
   Substituting $V$ into the voltage sensitivity equation:
   $$V_s = \frac{\phi}{IR} = \frac{1}{R} \left( \frac{\phi}{I} ight) = \frac{I_s}{R}$$
   Rearranging for Resistance ($R$):
   $$R = \frac{I_s}{V_s}$$
3. **Calculation:**
   - Given $I_s = 5 	ext{ div/mA} = 5 	imes 10^3 	ext{ div/A}$ (converting mA to A).
   - Given $V_s = 20 	ext{ div/V}$.
   - Substitute the values:
     $$R = \frac{5 	ext{ div/mA}}{20 	ext{ div/V}} = \frac{5}{20} \frac{	ext{V}}{	ext{mA}} = 0.25 	ext{ k}\Omega = 250 \, \Omega$$
     *Alternatively, using base units:* $R = \frac{5000}{20} = 250 \, \Omega$.

Step-by-Step Solution

Practice All PHYSICS Questions