Question

In the circuit sown in the figure switch S is closed at time t = 0. Select the wrong statement –

• A. Rate of increase of charge is same in both the capacitors
• B. Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2
• C. Time constants of both the capacitor are equal
• D. Steady state charge in capacitors C and 2C are in the ratio of 1 : 2

Answer 1

Answer: (A)

Rate of increase of charge is same in both the capacitors

Answer 2

Time constant

̃ $\tau_{C_{1}}$= 2CR

$\tau_{C_{2}}$= 2CR

q₁ = CE (1 – $e^{- \frac{t}{2CR}}$)

q₂ = 2CE (1 –$e^{- \frac{t}{2CR}}$)

\ $\frac{q_{1}}{q_{2}} = \frac{1}{2}$

$\frac{dq_{1}}{dt}$= $\frac{EC}{\tau_{C}}e^{- \frac{t}{\tau_{C}}}$

$\frac{dq_{2}}{dt}$= $\frac{2CE}{\tau_{C}}e^{- \frac{t}{\tau_{C}}}$

\ $\frac{dq_{1}}{dt}$¹ $\frac{dq_{2}}{dt}$