Question

60. A coil has an inductance of 53 mH and a resistance of 0.35S2. If a 12V emf is applied across the coil, how much energy is stored in the magnetic field after the current has built up to its equilibrium value ?
(A) 23 J
(B) 31 J
(C) 55 J
(D) 100 J

Answer 1

answer : option (B) 31 J

explanation : it is given that inductance, L = 53mH = 53 × 10^-3 H

resistance , R = 0.35Ω

emf (electromotive force) of battery, V = 12 volts.

first of all, find out current through inductor. i.e., I = V/R = (12/0.35) = 34.28 A

now, energy stored in the magnetic field after the current has built up to its equilibrium, E = 1/2 LI²

= 1/2 × 53 × 10^-3 × (34.28)²

≈ 31 J

hence, option (B) is correct choice.

Answer 2

The energy stored in the magnetic field is 31.14 Joules.

Explanation:

The formula of energy stored in the magnetic field after the current has built up to its equilibrium value is:

E = 1/2 LI²

Where,

L = Inductance = 53 mH (Given)

I = Current.

The current is given by the formula:

I = V/R

Where,

V = Voltage = 12 V (Given)

R = Resistance = 0.35 Ω (Given)

On substituting the values, we get,

I = 12/0.35 = 34.28 A

Now, the energy becomes,

E = 1/2 × 53 × 10⁻³ × (34.28)²

∴ E = 31.14 J