Question

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

• A. $500 \, \Omega$
• B. $40 \, \Omega$
• C. $250 \, \Omega$
• D. $25 \, \Omega$

Answer 1

The Correct Option is C

To determine the resistance of the moving coil galvanometer, we can use the relationship between current sensitivity, voltage sensitivity, and resistance. Here are the steps to solve the problem:

1. Understand the definitions:
   • Current sensitivity is defined as the deflection per unit current, given as 5 \, \text{div/mA}. This can also be expressed as 5 \, \text{div}/0.001 \, \text{A} since 1 mA = 0.001 A.
   • Voltage sensitivity is defined as the deflection per unit voltage, given as 20 \, \text{div/V}.
2. The relationship between current sensitivity (S_i), voltage sensitivity (S_v), and resistance (R) is given by:
   S_v = \frac{S_i}{R}
3. Substitute the given values into the formula:
   20 \, \text{div/V} = \frac{5 \, \text{div/mA}}{R}
   This equation converts to:
   20 = \frac{5}{R \times 0.001}
   Simplifying this gives:
   20 = \frac{5}{0.001R}
   R = \frac{5}{20 \times 0.001}
   R = \frac{5}{0.02}
   R = 250 \, \Omega
4. Thus, the resistance of the galvanometer is 250 \, \Omega. The correct option is 250 \, \Omega.

Conclusion: The resistance of the moving coil galvanometer is 250 \, \Omega, which matches the given correct answer option.