Question

Find the resistance required to be connected to a galvanometer of resistance \(100 \, \Omega\) with a full scale deflection of 1mA into a voltmeter of range 1V.

• A. \( 1000 \, \Omega \)
• B. \( 100 \, \Omega \)
• C. \( 900 \, \Omega \)
• D. \( 200 \, \Omega \)

Hint:

To convert a galvanometer into a voltmeter, calculate the resistance required using the full-scale voltage and current, and apply Ohm's law.

Answer 1

The Correct Option is A

To convert a galvanometer into a voltmeter, we need to connect a resistance \( R \) in series with the galvanometer. The total resistance \( R_{\text{total}} \) of the voltmeter will be the sum of the resistance of the galvanometer \( R_g = 100 \, \Omega \) and the series resistance \( R \). The current through the galvanometer for full-scale deflection is \( I_g = 1 \, \text{mA} \), and the full-scale voltage of the voltmeter is \( V = 1 \, \text{V} \). From Ohm's law: \[ V = I_g (R_g + R) \] Substituting the known values: \[ 1 = 0.001 \times (100 + R) \] Solving for \( R \): \[ 100 + R = \frac{1}{0.001} = 1000 \] Thus, \( R = 1000 - 100 = 900 \, \Omega \). Therefore, the resistance required to be connected is \( 1000 \, \Omega \).