Q168 / 180 · COMEDK 2025 (25 May Shift) · Physics
When current in an inductance is changed at a uniform rate from 15 A to 30 A in 3 s, the self-induced emf in the coil is 25 V. The change in energy of the coil during this process is:
- Correct answerA1687.5 J
- B3735.5 J
- C3375.5 J
- D1876.5 J
Solution
Rate of change of current: $\dfrac{di}{dt} = \dfrac{30 - 15}{3} = 5$ A/s
Self-induced emf: $e = L\dfrac{di}{dt}$
$25 = L \times 5 \Rightarrow L = 5$ H
Change in energy stored in the inductor:
$\Delta U = \dfrac{1}{2}L(i_f^2 - i_i^2) = \dfrac{1}{2} \times 5 \times (30^2 - 15^2)$
$= 2.5 \times (900 - 225) = 2.5 \times 675 = 1687.5$ J
Self-induced emf: $e = L\dfrac{di}{dt}$
$25 = L \times 5 \Rightarrow L = 5$ H
Change in energy stored in the inductor:
$\Delta U = \dfrac{1}{2}L(i_f^2 - i_i^2) = \dfrac{1}{2} \times 5 \times (30^2 - 15^2)$
$= 2.5 \times (900 - 225) = 2.5 \times 675 = 1687.5$ J
Hence, the correct answer is option: 'A'.