In the circuit shown in the figure, switches S1 and S2 have been closed for a long time.

Engineering

Physics

Electric Potential Energy and Electric Potential

Parallel Plate Capacitor

Basic Circuit Theory and Kirchoffs Law for DC Circuit

Question

In the circuit shown in the figure, switches S₁ and S₂ have been closed for a long time.

Charge on the capacitor remains unchanged if one third of the gap of the capacitor’s plates is filled with a dielectric (K = 2) of same area.

Charge on the capacitor increases to 120 μC if one third of the gap of the capacitor’s plates is filled with a dielectric (K = 2) of same area.

Charge on the capacitor is 20 μC

Charge on the capacitor is 100 μC

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After long time, capacitor is fully charged and acts as open circuit. The voltage across capacitor equals voltage across 10Ω resistor. Using voltage divider rule:

$V_{C} = 30 \times \frac{10}{10 + 20} = 10 V$

Charge $Q = C V_{C} = 10 μ F \times 10 V = 100 μ C$

Final answer: Charge on the capacitor is 100 μC