Question

The galvanometer resistance is 30 $\Omega$ and it is connected to 2 V battery along with a resistance 2000 $\Omega$ in series. A full scale deflection of 25 divisions is obtained. In order to reduce this deflection to 20 divisions, the resistance in series should be

• A. 2507 $\Omega$
• B. 2320 $\Omega$
• C. 2180 $\Omega$
• D. 2210 $\Omega$

Answer 1

The correct option is A 2507 $\Omega$

Total initial resistance = 30+2000=2030 ohm.
Battery voltage= 2v
Current =2/2030=$0.98\times {10}^{-3}$
Full scale deflection of 25 divisions was obtained .
In order to reduce this deflection to 20 divisions the resistor in series should be, current i= $\frac{20}{25}\times 0.98\times {10}^{-3}$ as full scale deflection for $0.98\times {10}^{-3}$ are 25 divisions.
Let the resistance be r ohm
$$2=2030\times 0.98\times {10}^{-3}=r\times \frac{20}{25}\times 0.98\times {10}^{-3}$$
$$r=2537ohm$$
Galvanometer resistance 30 ohm .
Resistance to be added (2537-30)=2507 ohm