Question

When a current of $5 \,mA$ is passed through a galvanometer having a coil of resistance $15 \, \Omega$, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range $0-10 \,V$ is :

• A. $1.985 \times 10^3 \, \Omega$
• B. $2.045 \times 10^3 \, \Omega$
• C. $2.535 \times 10^3 \, \Omega$
• D. $4.005 \times 10^3 \, \Omega$

Answer 1

The Correct Option is A

To convert a galvanometer into a voltmeter of desired range, a resistance is put in series with the galvanometer. The question requires us to find this resistance to enable the galvanometer to measure up to 10 V.

1. R_g = 15 \, \Omega is given, which is the resistance of the galvanometer.
2. The galvanometer shows full scale deflection at current I_g = 5 \, mA = 0.005 \, A.
3. The desired voltage range of the voltmeter is 0 - 10 \,V.
4. The formula to determine the series resistance R_s to convert the galvanometer into a voltmeter is given by: V = I_g (R_g + R_s)
5. Substituting the given values: 10 = 0.005 (15 + R_s)
6. Rearranging for R_s gives: 15 + R_s = \frac{10}{0.005} = 2000
7. Therefore: R_s = 2000 - 15 = 1985 \, \Omega

Thus, the value of the resistance that needs to be put in series with the galvanometer to convert it into a voltmeter of range 0-10 V is 1.985 \times 10^3 \, \Omega, which matches the correct answer.