Question

If only $2%$ of the total current passes through an ammeter having coil of resistance $R$, then the resistance of the shunt of an ammeter is

• A. $49R$
• B. $\dfrac{R}{50}$
• C. $\dfrac{R}{49}$
• D. $50R$

Hint:

Ammeter shunt resistance is always much smaller than the coil resistance.

Answer 1

The Correct Option is C

Step 1: Current distribution.
Let total current be $I$.
Current through ammeter coil:
\[ I_g = 0.02I \] Current through shunt:
\[ I_s = 0.98I \]
Step 2: Voltage equality condition.
\[ I_g R = I_s R_s \]
Step 3: Substituting values.
\[ 0.02I \cdot R = 0.98I \cdot R_s \] \[ R_s = \frac{0.02}{0.98}R = \frac{R}{49} \]
Step 4: Conclusion.
The shunt resistance is $\dfrac{R}{49}$.