In each of two coils the rate of change of the magnetic flux in a single loop is the same. The emf induced in coil 1, which has 159 loops, is 2.78 V. The emf induced in coil 2 is 4.11 V. How many loops does coil 2 have

250 loops

Explanation:

We know that induced emf, E = -NdФ/dt wnere N = number of turns and dФ/dt = rate of change of magnetic flux.

Let E₁, E₂ and N₁, N₂ be the emfs and number of turns of coils 1 and 2 respectively. Since dФ/dt is the same for both coils,

E₁ = -N₁dФ/dt  (1) and E₂ = -N₂dФ/dt (2)

Dividing (1) by (2), we have

E₁/E₂ = -N₁dФ/dt/-N₂dФ/dt = N₁/N₂

E₁/E₂ = N₁/N₂

N₂ = (E₂/E₁)N₁

Given that E = 2.78 V, N₁ = 159 loops and E₂ = 4.11 V,  

N₂ = (E₂/E₁)N₁ = (4.11/2.78)159 = 250 loops

e) none of the above answers are correct