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

Question

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

In steady state, both the capacitors are at the same potential. Therefore,

\frac{Q _{1}}{C _{1}} = \frac{Q _{2}}{C _{2}}

or

\frac{Q _{1}}{C} = \frac{Q _{2}}{2 C}

or

Q_{2} = 2 Q_{1} \dots

(i)
Also

Q_{1} + Q_{2} = Q \dots

(ii)
Solving (i) and (ii), we get

∴ Q_{1} = \frac{Q}{3}

and

Q_{2} = \frac{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 figure. Initially, the switch is open and $C_{1}$ holds charge $Q$ . The switch is closed. At steady state, the charge on each capacitor would be

$Q, 2 Q$

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

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

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

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

Q,2Q

3Q​,32Q​

23Q​,3Q

32Q​,34Q​

In steady state, both the capacitors are at the same potential. Therefore, C1​Q1​​=C2​Q2​​ or CQ1​​=2CQ2​​ or Q2​=2Q1​…(i) Also Q1​+Q2​=Q…(ii) Solving (i) and (ii), we get ∴Q1​=3Q​ and Q2​=32​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 figure. Initially, the switch is open and $C_{1}$ holds charge $Q$ . The switch is closed. At steady state, the charge on each capacitor would be

$Q, 2 Q$

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

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

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