A parallel circuit consists two ideal inductor of inductance L and 2L and a resistance R. At some instant the same current $I_{0}$ is flowing in both the inductor in same direction.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

Total heat produced in resistance is equal to $\frac{2}{3} L I_{0}^{2}$

Total heat produced in resistance is equal to $\frac{1}{3} L I_{0}^{2}$

Total charge flow through resistance is $\frac{4 L I_{0}}{3 R}$

Final current in both inductor is same and equal to $\frac{I_{0}}{3}$

answer is A, C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$2 L \frac{d i_{2}}{d t} = \frac{L d i}{d t} = (i_{1} + i_{2}) R$
Final current ‘i’
$2 (i_{0} - i) = i + i_{0}$
$i = i_{0} / 3$
Heat $= \frac{1}{2} (3 L) \frac{{i_{0}}^{2}}{9} - \frac{1}{2} 3 L i_{0}^{2}$
$= \frac{1}{2} 3 L i_{0}^{2} . \frac{8}{9} = \frac{4}{3} L i_{0}^{2}$
Charge $= \int (i_{1} + i_{2}) d t$