For ensuring dissipation of same energy in all three resistors ({R_1},,{R_2},,{R_3}) connected as shown in figure, their values must be related as

Q: For ensuring dissipation of same energy in all three resistors $({R_1},\,{R_2},\,{R_3})$ connected as shown in figure, their values must be related as

c (c) As the voltage in ${R_2}$ and ${R_3}$ is same therefore, according to, $H = \frac{{{V^2}}}{R}.t,$ ${R_2} = {R_3}$ Also the energy in all resistance is same. ${i^2}{R_1}t = i_1^2{R_2}t$ Using ${i_1} = \frac{{{R_3}}}{{{R_2} + {R_3}}}i = \frac{{{R_3}}}{{{R_3} + {R_3}}}i = \frac{1}{2}i$ Thus ${i^2}{R_1}t = \frac{{{i^2}}}{4}{R_2}t$ or, ${R_1} = \frac{{{R_2}}}{4}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

For ensuring dissipation of same energy in all three resistors $({R_1},\,{R_2},\,{R_3})$ connected as shown in figure, their values must 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 ${R_1} = \frac{1}{4}{R_2}$
D${R_1} = {R_2} + {R_3}$

AIIMS 2005, Diffcult

STD 11 Science
JEE
STD 12 - 3. current electricity
Physics

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