The amount of the charge passed in time t through a cross-section of a wire is \( Q_t = At^{2} + Bt + C \). If the value of A, B, C in SI units respectively are 5, 3, 1 the value of current at t = 5 s is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 53 A
The instantaneous current is the rate of flow of charge, \( I = dQ/dt \), so differentiate \( Q_t \) with respect to time.
\( Q_t = 5t^{2} + 3t + 1 \)
\( \displaystyle I = \frac{dQ_t}{dt} = 2At + B = 10t + 3 \)
At \( t = 5\,\mathrm{s} \):
\( I = 10 \times 5 + 3 = 53\,\mathrm{A} \)