Question

A galvanometer of resistance 30 $\Omega$ is connected to battery of emf 2V with 1970 $\Omega$ resistance in series. A full scale deflection of 20 divisions is obtained in the galvanometer. To reduce the deflection to 10 divisions, the resistance in series required is

• A. 4030 $\Omega$
• B. 4000 $\Omega$
• C. 3970 $\Omega$
• D. 2000 $\Omega$

Answer 1

Answer: (C)

3970 $\Omega$

Case 1 : $V=2$ volts $R_g=30\Omega$ $R_s=1970$

A full scale deflection of 20 divisions $\left(I_g\right)$ is obtained.

$\therefore$ $V=I_g(R_g+R_s)$

Or $2=I_g(30+1970)$

We get $I_g=0.001$ A

Case 2 : $V=2$ volts $R_g=30\Omega$

A full scale deflection of 10 divisions is obtained i.e. $\frac{I_g}{2}$ is obtained.

$\therefore$ $2=\frac{I_g}{2}(30+R_s^{\prime })$

Or $2=\frac{0.001}{2}(30+R_s^{\prime })$

Or $R_s^{\prime }+30=4000$

Thus we get $R_s=3970\Omega$