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, \({R_1} = \frac{{{R_2}}}{4}\)