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
Answers
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.
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