MCQ
Two identical capacitors $\mathrm{A}$ and $\mathrm{B}$, charged to the same potential $5\; \mathrm{V}$ are connected in two different circuits as shown below at time $\mathrm{t}=0$ If the charge on capacitors $A$ and $B$ at time $\mathrm{t}=\mathrm{CR}$ is $\mathrm{Q}_{\mathrm{A}}$ and $\mathrm{Q}_{\mathrm{B}}$ respectively, then (Here $e$ is the base of natural logarithm)
  • $\mathrm{Q}_{\mathrm{A}}=\mathrm{VC}, \mathrm{Q}_{\mathrm{B}}=\frac{\mathrm{VC}}{\mathrm{e}}$
  • 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
    $\mathrm{Q}_{\mathrm{A}}=\frac{\mathrm{VC}}{\mathrm{e}}, \mathrm{Q}_{\mathrm{B}}=\frac{\mathrm{CV}}{2}$

Answer

Correct option: A.
$\mathrm{Q}_{\mathrm{A}}=\mathrm{VC}, \mathrm{Q}_{\mathrm{B}}=\frac{\mathrm{VC}}{\mathrm{e}}$
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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