Question

A galvanometer with resistance 100 Ω gives full-scale deflection with a current of 2 mA. The resistance required to convert the galvanometer into an ammeter of range 0 to 20 A is nearly:

• A. 10$^{−2}$ Ω in series
• B. 10$^{−2}$ Ω in parallel
• C. 10$^{−1}$ Ω in parallel
• D. 10$^{−1}$ Ω in series

Answer 1

The Correct Option is B

To convert a galvanometer into an ammeter, we need to connect a shunt resistor in parallel with the galvanometer. The purpose of this shunt resistor is to allow most of the current (20 A in this case) to bypass the galvanometer, allowing it to measure higher currents without being damaged.

First, we calculate the full-scale voltage across the galvanometer, \( V_g \), using Ohm's Law: 

\( V_g = I_g \times R_g \)

Given \( I_g = 2 \, \text{mA} = 0.002 \, \text{A} \) and \( R_g = 100 \, \Omega \), we find:

\( V_g = 0.002 \, \text{A} \times 100 \, \Omega = 0.2 \, \text{V} \)

Next, to find the shunt resistance, \( R_s \), we use the formula:

\( R_s = \frac{V_g}{I - I_g} \)

Where \( I = 20 \, \text{A} \) is the total current through the ammeter:

\( R_s = \frac{0.2 \, \text{V}}{20 \, \text{A} - 0.002 \, \text{A}} \approx \frac{0.2 \, \text{V}}{19.998 \, \text{A}} \approx 0.01 \, \Omega \)

Thus, the correct resistance required to connect in parallel is approximately \( 10^{-2} \, \Omega \) to achieve the desired range. Hence, the correct answer is:

10$^{-2}$ Ω in parallel

Answer 2

\(\text{ To convert a galvanometer into an ammeter, a shunt resistance is connected in parallel with the galvanometer.}\)

\(\text{The shunt resistance } R_s \text{ is calculated using the formula:}\)

\(R_s = \frac{I_g R_g}{I - I_g}\) 

\(\text{Where: } I_g = 2 \, \text{mA} = 0.002 \, \text{A}, \, R_g = 100 \, \Omega, \, I = 20 \, \text{A}. \text{ Substituting the values into the formula:}\) 

\(R_s = \frac{0.002 \times 100}{20 - 0.002} = \frac{0.2}{19.998} \approx 0.01 \, \Omega\) 

\(\text{Thus, the required shunt resistance is approximately } 0.01 \, \Omega, \text{ which corresponds to option } 10^{-2} \, \Omega \text{ in parallel.}\)