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: Set up the parallel combination.
The shunt $S$ sits in parallel with the galvanometer $G$, and the result is the ammeter resistance $R_A$. So $\frac{1}{R_A}=\frac{1}{G}+\frac{1}{S}$.

Step 2: Rearrange for the shunt.
\[ \frac{1}{S}=\frac{1}{R_A}-\frac{1}{G}=\frac{1}{2.5}-\frac{1}{50} \]

Step 3: Combine the fractions.
$\frac{1}{2.5}=\frac{20}{50}$, so $\frac{1}{S}=\frac{20-1}{50}=\frac{19}{50}$.

Step 4: Invert.
$S=\frac{50}{19}\ \Omega$. \[ \boxed{\frac{50}{19}\ \Omega} \]