Question

A capacitor C₁ of capacitance 5 μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C₂ of capacitance 10 μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C₂ is ____ μC.

Answer 1

Correct Answer: 100

To find the charge on capacitor C₂ at equilibrium, we use the principle of conservation of charge. Initially, only capacitor C₁ is charged with a charge Q₁ given by the equation:
Q₁ = C₁V = 5μF × 30V = 150μC.

When the switch is closed, charge redistributes between C₁ and C₂. At equilibrium, the charge is shared between the two capacitors, and the total charge remains conserved.

Let Q' be the final charge on C₁ and Q'' be the final charge on C₂. Then:
Q' + Q'' = Q₁ = 150μC.

At equilibrium, the voltage across both capacitors is the same. Therefore:
V' = V''
C₁ × V' = Q'
C₂ × V'' = Q''
Q'/5 = Q''/10
2Q' = Q''

Using Q' + Q'' = 150μC and 2Q' = Q'', solve for the charges:
Q' + 2Q' = 150μC
3Q' = 150μC
Q' = 50μC
Q'' = 2Q' = 100μC.

Therefore, the charge on capacitor C₂ is 100μC.