$t=0$ સમયે બે સમાન કેપેસીટર $\mathrm{A}$ અને $\mathrm{B}$ ને સમાન $5\;V$ સાથે આકૃતિમાં દર્શાવ્યા પ્રમાણે જોડેલા છે.$\mathrm{t}=\mathrm{CR}$ સમયે $\mathrm{A}$ અને $\mathrm{B}$ કેપેસીટર પર વિજભાર $\mathrm{Q}_{\mathrm{A}}$ અને $\mathrm{Q}_{\mathrm{B}}$ હોય તો ....

Question

A$\mathrm{Q}_{\mathrm{A}}=\mathrm{VC}, \mathrm{Q}_{\mathrm{B}}=\frac{\mathrm{VC}}{\mathrm{e}}$
B$\mathrm{Q}_{\mathrm{A}}=\frac{\mathrm{CV}}{2}, \mathrm{Q}_{\mathrm{B}}=\frac{\mathrm{VC}}{\mathrm{e}}$
C$\mathrm{Q}_{\mathrm{A}}=\mathrm{VC}, \mathrm{Q}_{\mathrm{B}}=\mathrm{CV}$
D$\mathrm{Q}_{\mathrm{A}}=\frac{\mathrm{VC}}{\mathrm{e}}, \mathrm{Q}_{\mathrm{B}}=\frac{\mathrm{CV}}{2}$

JEE MAIN 2020, Medium

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Solution

a
For (A)

No current flows

Hence $Q_{A}=C V$

For $(\mathrm{B})$

$\mathrm{i}=\frac{\mathrm{V}}{\mathrm{R}} \mathrm{e}^{-\frac{\mathrm{t}}{\mathrm{RC}}}$

$\mathrm{q}=\mathrm{CV} \mathrm{e}^{\frac{\mathrm{t}}{\mathrm{RC}}}$

at $\mathrm{t}=\mathrm{CR}$

$\mathrm{Q}_{\mathrm{B}}=\mathrm{CV} \mathrm{e}^{-1}=\frac{\mathrm{CV}}{\mathrm{e}}$

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