The current in a long straight conductor varies with time according to the relation

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

The current in a long straight conductor varies with time according to the relation I(t)=10sin⁡ ⁣(πt2)+2I(t) = 10 \sin\!\left( \dfrac{\pi t}{2} \right) + 2, where II is in amperes and tt in seconds for the interval 0≤t≤4 s0 \le t \le 4\,\text{s}. (i) Sketch qualitatively the variation of II with tt for the given interval. (ii) Obtain an expression for the total charge that passes through a cross-section of the conductor from t=0t = 0 to t=4 st = 4\,\text{s}. (iii) Calculate the numerical value of this charge. (iv) Determine the average current in the interval and compare it with the instantaneous current at t=2 st = 2\,\text{s}. Comment on any difference you observe.

Related theory

Browse the problem library