Question

A moving coil galvanometer is converted into an ammeter of range 0 to 5mA. The galvanometer resistance is 90Ω and the shunt resistance has a value of 10Ω. If there are 50 divisions in the galvanometer-turnedammeter on either sides of zero, its current sensitivity is

• A. 1 × 10⁵ A/div
• B. 2 × 10⁴ A/div
• C. 1 × 10⁵ div/A
• D. 2 × 10⁴ div/A

Answer 1

The Correct Option is C

Given Information: 
Galvanometer resistance, \(G = 90\,\Omega\)
Shunt resistance, \(S = 10\,\Omega\)
Ammeter range, \(I = 5\,mA = 5 \times 10^{-3}\,A\)
Number of divisions on one side = \(50\) divisions

Step-by-Step Explanation:

Step 1: Find the galvanometer current (\(I_g\)) for full-scale deflection.

Using the formula for shunt resistance in galvanometer conversion:

\[ I_g \cdot G = (I - I_g) \cdot S \]

Substitute given values:

\[ I_g \times 90 = (5\times10^{-3} - I_g)\times10 \]

Solving for \(I_g\):

\[ 90\,I_g = 5\times10^{-2} - 10\,I_g \]

Bring terms involving \(I_g\) together:

\[ 90\,I_g + 10\,I_g = 5\times10^{-2} \]

\[ 100\,I_g = 5\times10^{-2} \]

Thus,

\[ I_g = \frac{5\times10^{-2}}{100} = 5\times10^{-4}\,A \]

Step 2: Find current sensitivity (divisions per ampere):

Number of divisions for full-scale deflection = \(50\) divisions

Thus, current sensitivity (\(S_I\)) is:

\[ S_I = \frac{\text{Number of divisions}}{I_g} = \frac{50}{5\times10^{-4}} = 1\times10^{5}\,\text{div/A} \]

Final Conclusion:
Current sensitivity is \(1\times10^{5}\,\text{divisions per ampere}\).