Current Electricity

A galvanometer having a coil resistance of 100 Ω gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A is:

  1. 2 Ω
  2. 0.1 Ω
  3. 3 Ω
  4. 0.01 Ω

Solution

Galvanometer is a very sensitive instrument therefore it cannot measure heavy currents. In order to convert a Galvanometer into an Ammeter, a very low shunt resistance is connected in parallel to Galvanometer. Value of shunt is so adjusted that most of the current passes through the shunt.

If resistance of galvanometer is Rg and it gives full-scale deflection when current Ig is passed through it. Then,

V = IgRg

V = 1 mA × 100 Ω

Let a shunt of resistance (Rs) is connected in parallel to galvanometer. If total current through the circuit is I.

I = 10 A = Is + Ig

V = IsRs = (I - Ig)Rs

(I - Ig)Rs = IgRg

(10 - 10-3)Rs = 100 × 10-3

Rs ≈ 0.01 Ω

The correct option is D.