Question

In an inductor of self-inductance L = 2 mH, current changes with time according to relation, I = t2ie-t. At what time emf is zero?

• A. 4 s
• B. 3 s
• C. 2 s
• D. 1 s

Answer 1

Answer: (C)

2 s

Answer 2

$L = 2mH = 2 \times 10^{- 3}H$

$I = t^{2}e^{- t}$

$\frac{dI}{dt} = t^{2}e^{- t}( - 1) + e^{- t}(2t) = te^{- t}( - t + 2)$

emf $= L\frac{dI}{dt} = 2 \times 10^{- 3}te^{- t}( - t + 2)$

Now, emf $( - t + 2) = 0$ $t = 2s$