Question

Find the total heat produced in the loop of the previous problem during the interval 0 to 30 s if the resistance of the loop is 4.5 mΩ.

Answer 1

Total Heat Produced is $2 \times 10^-^4 J$

Explanation:

Resistance of the coil, R = $45 m\Omega = 4.5 \times 10^-^3 \Omega$

The heat produced is found by taking the sum of the individual heats produced.

Thus, the net heat produced is given by

H = $H_1 + H_2 + H_3 + H_3$

(a) Heat developed for the first 5 seconds:

Emf induced, e = $3 \times 10^-^4 V$

Current in the coil, $I = \frac {e}{R}$

= $\frac {3 \times 10^-^4}{4.5 \times 10^-^3}$

$H_1 = (6.7 \times 10^-^2)^2 \times 4.5 \times 10^-^3 \times 5$

There is no change in the emf from 5 s to 20 s and from 25 s to 30 s.

Thus, the heat developed for the above mentioned intervals is given by

$H_2 = H_4 = 0$

Heat developed in interval t = 25 s to 30 s:

The current and voltage induced in the coil will be the same as that for the first 5 seconds.

$H_3 = (6.7 \times 10^-^2)^2 \times 4.5 \times 10^-^3 \times  5$

Total heat produced:

$H = H_1 + H_3$

   = $2 \times (6.7 \times 10^-^2)^2 \times 4.5 \times  10^-^2 \times 5$

   = $2 \times 10^-^4 J$