Question

A galvanometer of resistance 50 \( \Omega \) is converted into a voltmeter of range (0 — 2V) using a resistor of 1.0 k\( \Omega \). If it is to be converted into a voltmeter of range (0 — 10 V), the resistance required will be:

• A. 4.8k \( \Omega \)
• B. 5.0k \( \Omega \)
• C. 5.2k \( \Omega \)
• D. 5.4k \( \Omega \)

Hint:

To convert a galvanometer into a voltmeter, the total resistance required for the desired voltage range is calculated by using the current corresponding to the given voltage ranges. The series resistance is added to the galvanometer resistance.

Answer 1

The Correct Option is C

Given:
\( R_g = \SI{50}{\ohm} \)
\( R_s = \SI{1.0}{\kilo\ohm} = \SI{1000}{\ohm} \)
\( V_1 = \SI{2}{\volt} \)
\( V_2 = \SI{10}{\volt} \) Current through the galvanometer: \[ I = \frac{V_1}{R_g + R_s} = \frac{2}{1050} \, \si{\ampere} \] Total resistance for \SI{10}{\volt} range: \[ R_{\text{total}} = \frac{V_2}{I} = \frac{10}{\frac{2}{1050}} = \SI{5250}{\ohm} \] Additional resistance required: \[ R_{\text{new}} = R_{\text{total}} - R_g = \SI{5250}{\ohm} - \SI{50}{\ohm} = \SI{5.2}{\kilo\ohm} \] Answer: \boxed{\text{(C) } \SI{5.2}{\kilo\ohm}}