Q.
For ensuring dissipation of same energy in all three resistors $(R_{1},R_{2},R_{3})$connected as shown in figure, their values be related as
A) $R_{1} = R_{2} = R_{3}$
B) $R_{2} = R_{3}$ and $R_{1} = 4\ R_{2}$
C) $R_{2} = R_{3}$ and $R_{1}{= R}_{2}/4$
D) $R_{1} = \ $ $R_{2} + R_{3}$
Explanation
(c) As voltage across the resistors $R_{2}\ and\ R_{3}$ is same and they show same dissipation of energy, so using the relation for energy, $H = \frac{V^{2}}{R}t,\ we\ have\ R_{2} = R_{3}$. Thus, the current in each resistor $R_{2}\ and\ R_{3}\ will\ be\ I/2$
$ie,I_{1} = I$/2 and $I_{2} = I$/2
[image:3_image161.emf]
Since the energy dissipation is same in all the three resistors, so
${\ I}^{2}R_{1}t = I_{1}^{2}R_{2}t$
or $I^{2}R_{1}t = (I/2)^{2}R_{2}t$
or $R_{1} = R_{2}$/4
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.