Question

A galvanometer of resistance \(50\,\Omega\) gives full-scale deflection when a current of \(2\,\text{mA}\) passes through it. The value of shunt resistance required to convert it into an ammeter of range \(2\,\text{A}\) is

• A. \(0.05\,\Omega\)
• B. \(0.5\,\Omega\)
• C. \(5\,\Omega\)
• D. \(50\,\Omega\)

Hint:

To convert a galvanometer into an ammeter: \[ \boxed{S=\frac{I_gG}{I-I_g}} \] Ammeter \(\Rightarrow\) Low resistance Hence a small shunt resistance is connected in parallel.

Answer 1

The Correct Option is A

Step 1: Recall the shunt formula for ammeter conversion. \[ S=\frac{I_gG}{I-I_g} \] where \[ I_g=2\times10^{-3}\,\text{A} \] \[ G=50\,\Omega \] \[ I=2\,\text{A} \]

Step 2: Substitute the values. \[ S=\frac{(2\times10^{-3})(50)}{2-0.002} \] \[ S=\frac{0.1}{1.998} \] \[ S\approx0.05\,\Omega \]

Step 3: Identify the correct option. \[ \boxed{S=0.05\,\Omega} \] Therefore, \[ \boxed{\text{(A)}} \] is the correct answer.