Question

A galvanometer of resistance \(200 \Omega\) gives full scale deflection for a current of \(10^{-3} \mathrm{~A}\). To convert it into an ammeter capable of measuring upto \(1 \mathrm{~A}\). What resistance should be connected in parallel with it ? (A) \(2 \times 10^{-1} \Omega\) (B) \(2 \Omega\) (C) \(2 \times 10^{-3} \Omega\) (D) \(2 \times 10^{-6} \Omega\)

Short answer

The correct answer is \( (A) 2 \times 10^{-1} \Omega \), as the shunt resistance calculated to convert the galvanometer into an ammeter capable of measuring up to 1 A is approximately \( 0.2004 \Omega \).

Step-by-step solution

Understand the concept of the shunt#:

The shunt is a low resistance connected in parallel with the galvanometer that allows most of the current to pass through it. This allows the galvanometer to measure higher currents without damaging or affecting the galvanometer's measurements. In this case, we want to measure up to 1 A with a galvanometer that has a full-scale deflection current of \(10^{-3} A. \)

Identify the given parameters#:

We are given the following values: Galvanometer resistance, \(R_G = 200 \Omega\) Galvanometer full-scale deflection current, \(I_G = 10^{-3} A\) Maximum current to be measured, \(I_A = 1 A\)

Calculate the shunt resistance#:

To calculate the shunt resistance, we will use the following formula derived from the principle of parallel resistance: \(R_S = \frac{R_G \cdot I_G}{I_A - I_G}\) Substitute the given values: \(R_S = \frac{200 \cdot 10^{-3}}{1 - 10^{-3}}\)

Find the value of the shunt resistance#:

Now, let's calculate the value of the shunt resistance: \(R_S = \frac{200 \cdot 10^{-3}}{1 - 10^{-3}} \approx 0.2004 \Omega\)

Choose the correct answer from the given options#:

Since we have found the value of the shunt resistance, we can now choose the correct option. The calculated value is approximately \(0.2004 \Omega\), which is closest to option (A) \(2 \times 10^{-1} \Omega\). Therefore, the correct answer is option (A).