MHT CET · Physics · Current Electricity

A galvanometer of resistance $30 Ω$ is connected to a battery of emf $2 V$ with $1970 Ω$ 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 $4030 Ω$
B $4000 Ω$
C $3970 Ω$
D $2000 Ω$

Verified Solution

Answer & Solution

Correct Answer

(C) $3970 Ω$

Step-by-step Solution

Detailed explanation

i = \frac{V}{R_{e f f}} = \frac{V}{1970 + 30} = \frac{2}{2000} = 1 \times 10^{- 3} A = 1 m A

This current provides full scale deflection (i.e. 20 division) In order to limit the deflection 10 divisions,
the resistances needed to connect can be obtained as

θ = \frac{n i A B}{k}

∴ \frac{θ_{1}}{θ_{2}} = \frac{i_{1}}{i_{2}}

∴ θ_{1} : θ_{2} = 2

∴ i_{1} : i_{2} = 2:1

∴ i_{2} = \frac{i_{1}}{2} = \frac{1 \times 10^{- 3}}{2} = 5 \times 10^{- 4} m A

∴ i = \frac{V}{R_{e f f} + R s} \Rightarrow R s = \frac{V}{i} - R_{e f f}

= \frac{2}{5 \times 10^{- 4}} - 2000

= \frac{2}{5} \times 10^{4} - 2000

= 4 \times 10^{3} - 2000

= 2000 Ω

∴

The resistance of

1970 Ω

is to be replaced by

1970 + 2000 = 3970 Ω

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app

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

Step-by-step Solution

A galvanometer of resistance $30 Ω$ is connected to a battery of emf $2 V$ with $1970 Ω$ 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