Question

Two moving coil galvanometers G₁ and G₂ are identical except for the following features:

Features	G1	G2
Number of turns	50	60
Area of the coil	30 cm2	40 cm2
Resistance of the coil	4 Ω	6 Ω

Perform calculations to determine which galvanometer has greater current sensitivity.

Answer 1

To determine which galvanometer has greater current sensitivity, we use the formula for the current sensitivity of a moving coil galvanometer:

S = `(NBA)/(kR)`

Given that the two galvanometers have the same magnetic field strength (B) and the same constant (k), we can compare their current sensitivities using the remaining parameters: the number of turns (N), the area of the coil (A), and the coil resistance (R).

The relative sensitivity for G₁.

N₁ = 50

A₁ = 30 cm²

R₁ = 4 Ω

`S_1 = (N_1 xx A_1)/(R_1)`

= `(50 xx 30)/4`

= `1500/4`

= 375

The relative sensitivity for G₂.

N₂ = 60

A₂ = 40 cm²

R₂ = 6 Ω

`S_2 = (N_2 xx A_2)/(R_2)`

= `(60 × 40)/6`

= `2400/6` 

= 400

∴ S₂ > S₁ 

400 > 375

Because the galvanometer G₂ has greater current sensitivity than the galvanometer G₁.