A galvanometer of resistance `30Omega` is connected to a battery of emf 2 V with `1970Omega` 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

Options

A. `4030 Omega`
B. `4000 Omega`
C. `3970 Omega`
D. `2000 Omega`

Answer

C

Explanation

The initial current in G is `I_1=2/(1970+30)=1/(1000)A` The deflection `theta` is directly proportional to I. `therefore` If the deflection becomes half (from 20 to 10 div), then`I_2=I_1/2=1/2000A` Foe this the total resistance in the circuit is `I_2=1/2000=2/X therefore X=4000Omega` But X=galvanometer resistance+series resistance `therefore 4000=30+R_S therefore R_S=3970 Omega`.