Q.
Arrange the order of power dissipated in the given circuits, if the same current is passing through all the circuits. The resistance of each resistor is $r$.
A) $P_{1}{> P}_{2} > P\ _{3} > P_{4}$
B) $P_{2}{> P}_{3} > P\ _{4} > P_{1}$
C) $P_{4}{> P}_{3} > P\ _{2} > P_{1}$
D) $P_{1}{= P}_{2} = P\ _{3} = P_{4}$
Explanation
(b) Here $P_{1} = i^{2} \times \frac{r}{3},\ P_{2} = i^{2} \times 3r$,
$P_{3} = i^{2}\left( \frac{r}{2} + r \right) = \frac{3}{2}i^{2}r$
and $P_{4} = i^{2}\left\lbrack \frac{2r \times 2r}{2r + 2r} \right\rbrack = i^{2}r$
So it is obvious that $P_{2} > P_{3} > P_{4} > P_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.