Physics

Problem

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

I(t) = 10 \sin\!\left( \dfrac{\pi t}{2} \right) + 2

, where

I

is in amperes and

t

in seconds for the interval

0 \le t \le 4\,\text{s}

. a. (i) Sketch qualitatively the variation of

I

with

t

for the given interval. b. (ii) Obtain an expression for the total charge that passes through a cross-section of the conductor from

t = 0

t = 4\,\text{s}

. c. (iii) Calculate the numerical value of this charge. d. (iv) Determine the average current in the interval and compare it with the instantaneous current at

t = 2\,\text{s}

. Comment on any difference you observe.

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