Question

Two capacitors of capacities 2 µF and 4 µF are connected in parallel. A third capacitor of 6µF capacity is connected in series with this combination. A battery of 12 V is connected across this combination. The charge on 2µF capacitor is ______.

Options

• 12 µC

• 11 µC

• 14 µC

• 16 µC

Answer 1

Two capacitors of capacities 2 µF and 4 µF are connected in parallel. A third capacitor of 6µF capacity is connected in series with this combination. A battery of 12 V is connected across this combination. The charge on 2µF capacitor is 12 µC.

Explanation:

The circuit diagram of given situation is as shown below

The equivalent capacitance of 2µF and 4µF capacitors connected in parallel Is

C_eq = 2 + 4 = 6µF

The circuit now becomes

As, both the capacitors are of the same capacitance, so the potential of 12 V is equally divided in them i.e.,

V₁ = V₂ = 6V

In parallel combination, the potential remains the same.

∴ Charge on 2µF, Q = 2 × V₁ = 2 × 6 = 12µC

OR

 

Let C₁ = 2µF, C₂ = 4µF and C₃ = 6µF

Equivalent of C₁ and C₂ = C₄ = 6µF

Equivalent of C₃ and C₄ = C₅ = 3µF

Charge on C₅ = Q = C₅ V = 3 × 12 = 36 µC.

C₃ and C₄ are in series. Hence charge on them is also 36 µC.

The charge of 36 µC is divided between C₁ and C₂ in proportion to their capacitance.

`Q_1/Q_2 = C_1/C_2`

∴ `Q_1/(Q_1 + Q_2) = C_1/(C_1 + C_2)`

∴ `Q_1/Q = C_1/(C_1 + C_2) = 2/6 = 1/3`

∴ `Q_1 = Q/3 = 36/3 = 12muC`