Question

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t=0, then the energy stored in the coil after 4 s is _________ J.

Hint:

Unlike a resistor which dissipates energy as heat, an inductor stores energy in its magnetic field as long as current is flowing.

Answer 1

Correct Answer: 144

Step 1: Voltage across inductor $V = L \frac{di}{dt}$.
Step 2: $3t = 2 \frac{di}{dt} \Rightarrow di = \frac{3}{2} t \, dt$.
Step 3: Integrate: $i = \int_0^4 \frac{3}{2} t \, dt = \frac{3}{2} \left[ \frac{t^2}{2} \right]_0^4 = \frac{3}{4} (16) = 12$ A.
Step 4: Energy stored $U = \frac{1}{2} L i^2 = \frac{1}{2} (2) (12^2) = 144$ J.