Question

A galvanometer of \( 50\Omega \) resistance is converted into an ammeter using a shunt resistance of \( 10\Omega \). If the same resistance is used to convert the same galvanometer into a voltmeter, what would be the ratio of the resistance of the ammeter to the resistance of the voltmeter?

• A. \( 5 : 1 \)
• B. \( 5 : 36 \)
• C. \( 5 : 6 \)
• D. \( 1 : 5 \)

Hint:

Ammeter uses parallel (low resistance), voltmeter uses series (high resistance). Always apply correct combination formulas.

Answer 1

The Correct Option is B

Step 1: Given values.
Galvanometer resistance: \( G = 50\Omega \), shunt resistance: \( S = 10\Omega \).

Step 2: Resistance of ammeter.
Ammeter is formed by parallel combination of \( G \) and \( S \):
\[ R_A = \frac{GS}{G+S} \]

Step 3: Substitute values.
\[ R_A = \frac{50 \times 10}{50 + 10} \]
\[ R_A = \frac{500}{60} = \frac{25}{3}\Omega \]

Step 4: Resistance of voltmeter.
Voltmeter is formed by series combination:
\[ R_V = G + S = 50 + 10 = 60\Omega \]

Step 5: Write ratio.
\[ \frac{R_A}{R_V} = \frac{\frac{25}{3}}{60} \]

Step 6: Simplify ratio.
\[ = \frac{25}{180} = \frac{5}{36} \]

Step 7: Final Answer.
\[ \boxed{5 : 36} \]