Question

A galvanometer has a coil of resistance \(200 \, \Omega\) with a full scale deflection at \(20 \, \mu A\). The value of resistance to be added to use it as an ammeter of range (0–20) mA is:

• A. \(0.40 \, \Omega\)
• B. \(0.20 \, \Omega\)
• C. \(0.50 \, \Omega\)
• D. \(0.10 \, \Omega\)

Answer 1

The Correct Option is B

Step 1: Formula for shunt resistance The shunt resistance \( R_s \) is given by:

\[ R_s = \frac{I_g R_g}{I - I_g}, \]

where:

• \( I_g = 20 \, \mu A = 20 \times 10^{-6} \, \text{A} \) (full-scale deflection current),
• \( R_g = 200 \, \Omega \) (resistance of the galvanometer),
• \( I = 20 \, mA = 20 \times 10^{-3} \, \text{A} \) (ammeter range).

Step 2: Substitute the values

\[ R_s = \frac{(20 \times 10^{-6}) \cdot 200}{(20 \times 10^{-3}) - (20 \times 10^{-6})}. \]

Simplify the numerator:

\[ (20 \times 10^{-6}) \cdot 200 = 4 \times 10^{-3}. \]

Simplify the denominator:

\[ (20 \times 10^{-3}) - (20 \times 10^{-6}) = 19.98 \times 10^{-3}. \]

Thus:

\[ R_s = \frac{4 \times 10^{-3}}{19.98 \times 10^{-3}} \approx 0.20 \, \Omega. \]

Final Answer: \( 0.20 \, \Omega. \)