Two coils C1 and C2 are placed close to each other. The magnetic flux Φ2 linked with the coil ​

Question

Two coils C₁ and C₂ are placed close to each other. The magnetic flux\(\phi _2\) linked with the coil C₂ varies with the current I₁, flowing in coil C₁, as shown in the figure. Find

(i) the mutual inductance of the arrangement, and

(ii) the rate of change of current \(\left(\frac{dI_1}{dt}\right)\)that will induce an emf of 100 V in coil C₂.

Answer 1

(i) we know that

\(\phi _2 = M_{12}I_1\)

From the given graph at any instant

\(I_1 = 2A , \phi _2 = 5\text{ wb}\)

On putting these value in equation

5 = M₁₂ × 2

M₁₂ = 2.5 H

(ii) We know that emf induced in secondary \(E_2 = - M_{12} \frac{dI_1}{dt}\)

Here, E₂ = 100 V, M₁₂ = 2.5 H

On putting these values in above equation \(100 = - 2.5 \frac{dI_1}{dt}\)

\(\frac{dI_1}{dt} = -40 \ \text{A/s}\)