Question

A galvanometer of resistance 50 $\Omega$ is converted to an ammeter. After shunting, the effective resistance of ammeter is 2.5 $\Omega$. The value of shunt is

• A. $\frac{100}{19}\ \Omega$
• B. $\frac{50}{19}\ \Omega$
• C. $\frac{25}{19}\ \Omega$
• D. $\frac{75}{19}\ \Omega$

Hint:

You can use the parallel product-over-sum shortcut directly: $R_A = \frac{G \cdot S}{G + S}$. Plugging in the numbers: $2.5 = \frac{50S}{50+S} \implies 125 + 2.5S = 50S \implies 47.5S = 125 \implies S = \frac{50}{19}\ \Omega$. Keeping fraction substitutions clear avoids decimal division step clutter!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given the internal resistance of a galvanometer ($G = 50\ \Omega$) and the final total equivalent resistance of the converted ammeter ($R_A = 2.5\ \Omega$). We need to find the value of the parallel shunt resistance ($S$) used.

Step 2: Detailed Explanation:
To convert a galvanometer into an ammeter, a very low shunt resistance $S$ is connected in parallel with the galvanometer coil. The total effective resistance $R_A$ of this parallel circuit combination is given by: $$ \frac{1}{R_A} = \frac{1}{G} + \frac{1}{S} \implies \frac{1}{S} = \frac{1}{R_A} - \frac{1}{G} $$ Substituting our given values ($R_A = 2.5\ \Omega$ and $G = 50\ \Omega$): $$ \frac{1}{S} = \frac{1}{2.5} - \frac{1}{50} $$ Convert the decimal fraction to simplify: $\frac{1}{2.5} = \frac{10}{25} = \frac{20}{50}$. $$ \frac{1}{S} = \frac{20}{50} - \frac{1}{50} = \frac{19}{50} $$ Inverting the fraction to solve for $S$: $$ S = \frac{50}{19}\ \Omega $$

Step 3: Final Answer:
The resistance value of the shunt is $\frac{50}{19}\ \Omega$, which corresponds to option (B).