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A galvanometer is tested shown in figure, in the circuit where, E = 1·5V R1 = 1·0 ohm, R2 = 2500 ohm and R3 is variable. With R3 set at 450 ohm, the galvanometer deflection is 140 mm and with R3 set at 950 ohm, the galvanometer deflection is 70 mm. The resistance of the galvanometer is:
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- 99 ohm
- 49 ohm
- 25 ohm
- 10 ohm
- 99 ohm
Correct Option: C
Given, E = 1·5V
R2 = 2500Ω
R1 = 1Ω
R3 = variable
RΩ = ?
From given figure
| I = | = | ||
| Req | [(R3 + RG)//R1] + R2 |
or
| I = | |
| R2 + {(R3 + RG)R1}/R3 + RGR1 |
or
| I = | |
| (R3 + RG + R1) + R2(R3 + RG)R1 |
Now, Galvanometer current is given by relation
| IG = I × | |
| R3 + RG |
when R3 = 450Ω, IG = 140 mm and
when R3 = 950Ω, IG = 70 mm
Applying these conditions, and manipulating the given parameters.
We get RG ≈ 49Ω.
