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) \[{{R}_{1}}={{R}_{2}}+{{R}_{3}}\]
Correct Answer: C
Solution :
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, \[{{R}_{1}}=\frac{{{R}_{2}}}{4}\]You need to login to perform this action.
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