Question

A galvanometer of resistance 20Ω gives a full-scale deflection when a current of 0.04 A is passed through it. To convert it into an ammeter of range 20A, the resistance that must be connected in series with the coil of the galvanometer is ______ 

(Galvanometer is shunted by 0.05 Ω) 

विकल्प

• 4.95 Ω

• 9.45 Ω

• 5.94 Ω

• 12.62 Ω

Answer 1

A galvanometer of resistance 20Ω gives a full-scale deflection when a current of 0.04 A is passed through it. To convert it into an ammeter of range 20A, the resistance that must be connected in series with the coil of the galvanometer is 4.95 Ω.

Explanation:

I_g = 0.04 A, I = 20 A, G = 20 Ω, S = 0.05 Ω 

Let resistance R be connected in series with the galvanometer coil, so that the effective resistance of the galvanometer is

G' = G + R

We have `I_g/I_s = S/G^'`

∴ `I_g/(I_g + I_s) = S/(S + G^')`

or `I_g/I = S/(S + G^')  "or" I/I_g = (S + G^')/S = 1 + G^'/S`

∴ `20/0.04 = 1 + G^'/S`

∴ `500 = 1 + G^'/S`

∴ `G^'/S = 466` or

G' = 499 × 0.05 = 24.95 Ω 

∴ R = 24.95 - 20 = 4.95 Ω