Two capacitors C1 and C2=2 C1 are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and C1 holds charge Q. The switch is closed. At steady state, the charge on each capacitors will be

Question

Two capacitors C1 and C2=2 C1 are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and C1 holds charge Q. The switch is closed. At steady state, the charge on each capacitors will be (A) Q, 2 Q (B) (Q/3), (2 Q/3) (C) (3 Q/2), 3 Q (D) (2 Q/3), (4 Q/3)

Tardigrade Admin · Accepted Answer

Charge redistributes on the capacitors in the ratio of their capacitance. (Q1/Q2)=(C1/C2)=(C1/2 C1)=(1/2) Q1: Q2=1: 2 ∴ Q1=(1/1+2) × Q=(Q/3) Q2=(2/1+2) Q=(2/3) Q

Q. Two capacitors $C_{1}$ and $C_{2} = 2 C_{1}$ are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and $C_{1}$ holds charge $Q$ . The switch is closed. At steady state, the charge on each capacitors will be

$Q, 2 Q$

$\frac{Q}{3}, \frac{2 Q}{3}$

$\frac{3 Q}{2}, 3 Q$

$\frac{2 Q}{3}, \frac{4 Q}{3}$

Charge redistributes on the capacitors in the ratio of their capacitance.
$\frac{Q _{1}}{Q _{2}} = \frac{C _{1}}{C _{2}} = \frac{C _{1}}{2 C _{1}} = \frac{1}{2}$
$Q_{1} : Q_{2} = 1 : 2$
$∴ Q_{1} = \frac{1}{1 + 2} \times Q = \frac{Q}{3}$
$Q_{2} = \frac{2}{1 + 2} Q = \frac{2}{3} Q$

Q. Two capacitors C1​ and C2​=2C1​ are connected in a circuit with a switch between them as shown in the figure. Initially the switch is open and C1​ holds charge Q. The switch is closed. At steady state, the charge on each capacitors will be

Q,2Q

3Q​,32Q​

23Q​,3Q

32Q​,34Q​