d
\(U\,\, = \,\,\frac{1}{2}C{V^2}\,\,\, \Rightarrow \frac{{{U_0}}}{2}\,\, = \,\,\frac{1}{2}C{V_0}^2{e^{ - 2{t_1}/RC}}\,\)

\(\, \Rightarrow \frac{1}{2}\,\, = \,\,{e^{ - 2{t_1}/RC}}\,\,\,\,[\because \,\,{U_0}\,\, = \,\,\frac{1}{2}C{V_0}^2]\)

\(\therefore  - \frac{{2{t_1}}}{{RC}}\,\, = \,\,\ln 2\,\,\, \Rightarrow {t_1}\,\, = \,\,\frac{{RC\ln 2}}{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,..........\,\,(i)\,\)

અને \(\frac{{{q_0}}}{4}\,\, = \,\,{q_0}{e^{ - {t_2}/RC}}\)

\( - \frac{{{t_2}}}{{RC}}\,\, = \,\,2\ln 2\,\,\,\, \Rightarrow {t_2}\,\, = \,\,2RC\ln 2\,\,\,\,\,\,\,\,\,\,\,...........\,\,(ii)\)

સમીકરણ \((i)\)અને \((ii)\) પરથી;

\([ \frac{{{t_1}}}{{{t_2}}}\,\, = \,\,\frac{1}{4}]\)