Question

The current in a wire varies with time according to the equation I = 4 + 2t, where I is in ampere and t is in sec. The quantity of charge which has passed through a cross-section of the wire during the time t = 2 sec to t = 6 sec will be

• A. 60 coulomb
• B. 24 coulomb
• C. 48 coulomb
• D. 30 coulomb

Answer 1

Answer: (C)

48 coulomb

Answer 2

Let dq be the charge which has passed in a small interval of time dt, then dq = idt = (4 + 2t)dt

Hence total charge passed between interval t = 2 sec and t = 6 sec q = $\int_{2}^{6}{(4 + 2t)dt}$ = 48 coulomb, Hence correct answer is

Energy stored in the coil = $\frac{1}{2}$ $LI_{0}^{2}$ = $\frac{1}{2}$ L $\left( \frac{E^{2}}{R^{2}} \right)$ = $\frac{1}{2}$

$\left( \frac{L}{R} \right)$ $\left( \frac{E^{2}}{R} \right)$ = $\frac{1}{2}$ tP

= total heat produced in the coil