JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Current Electricity

Two identical capacitors A and B, charged to the same potential 5 V are connected in two different circuits as shown below at time

t = 0

. If the charge on capacitors

A

and

B

at time

t = C R

Q_{A}

and

Q_{B}

respectively, then (Here e is the base of natural logarithm)

Answer: (C)

Solution

In circuit A the diode is reverse biased, so no discharge path exists and the capacitor keeps the charge it began with,

Q_{A} = C V

. In circuit B the diode is forward biased, so the capacitor discharges through the resistor and its charge decays as

q (t) = C V e^{- t / R C}

. At the instant

t = C R

this leaves

Q_{B} = C V e^{- 1} = \frac{C V}{e}

. Hence

Q_{A} = V C

and

Q_{B} = \frac{V C}{e}

JEE Main · 2020 · 09 Jan 2020 · Shift 2 · Single correct option