Question

An ammeter is obtained by shunting an \( n \, \Omega \) galvanometer with \( n \, \Omega \) resistance. The additional shunt required to be connected across it to double the range is

• A. \( \frac{n}{3} \)
• B. \( n \)
• C. \( \frac{n}{4} \)
• D. \( \frac{n}{2} \)

Hint:

When doubling the range of an ammeter, the shunt resistance needs to be calculated based on the original shunt resistance and the desired change in range.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
An ammeter is created by shunting a galvanometer. The total current through the circuit is divided between the galvanometer and the shunt. The resistance of the shunt controls the range of the ammeter. In this case, the galvanometer is shunted with resistance \( n \, \Omega \), and the range is to be doubled. Step 2: Relationship for doubling the range.
For a given galvanometer with a shunt resistance \( n \), the total current \( I_{\text{total}} \) passing through the circuit is divided between the galvanometer and the shunt. To double the range, the additional shunt resistance \( R_{\text{new}} \) needed is derived from the formula: \[ R_{\text{new}} = \frac{n}{3} \] Step 3: Conclusion.
Therefore, the additional shunt required to double the range is \( \frac{n}{3} \), which corresponds to option (A).