Two moving coil galvanometers G1 and G2 have the . . .

Question : Two moving coil galvanometers G1 and G2 have the following particulars respectively : 

N₁=30, A₁=3.6×10^-3 m², B₁=0.25 T

N₂=42, A₂=1.8×10^-3 m², B₂=0.50 T

The spring constant is same for both the galvanometers. The ratio of current sensitivities of G₁ and G₂ is : 

a) 5:7

b) 7:5

c) 1:4

d) 1:1 

Doubt by Trishna

Solution :

We know, 

current sensitivity is given by 
I_s = Φ/I = NBA/k

So 

I₁=N₁B₁A₁/k — (1)
I₂=N₂B₂A₂/k — (2)

Dividing equation (1) by equation (2)

I₁/I₂ = [N₁B₁A₁/k]/[N₂B₂A₂/k]

I₁/I₂ = [N₁B₁A₁]/[N₂B₂A₂]
I₁/I₂ = [N₁/N₂]×[B₁/B₂]×[A₁/A₂]
I₁/I₂ = [30/42]×[0.25/0.50]×[3.6×10^-3 / 1.8×10^-3]|
I₁/I₂ = [5/7]×[1/2]×[2]
I₁/I₂ = 5/7
I₁:I₂ = 5:7

Hence, (a) 5:7, would be the correct option.