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A parallel-plate capacitor is charged to V0 = 1350 V and then connected in parallel to an identical uncharged capacitor filled with a dielectric of constant k. After connection, the voltage across the first capacitor becomes 450 V and the charge on the second capacitor becomes 18 mC. Which of the following statements is/are correct?

1. The initial charge on the first capacitor is 27 mC
2. The dielectric constant k = 2
3. The charge on the first capacitor after connection is 18 mC
4. Heat loss is zero in this process

Correct answer: The initial charge on the first capacitor is 27 mC

Solution

Let capacitance of original capacitor = C. After connection at voltage 450 V: charge on C1 = C*450 = Q1_new; charge on C2 = k*C*450 = 18 mC. Total charge (conserved) = C*1350 = C*450 + k*C*450 = C*450*(1+k). So 1350 = 450*(1+k) => 1+k = 3 => k = 2. From k*C*450 = 18 mC: 2*C*450 = 18 mC => C = 18/(900) mC/V = 0.02 mF = 20 uF. Initial charge Q0 = C*1350 = 20e-6 * 1350 = 27 mC. Charge on C1 after = C*450 = 20e-6 * 450 = 9 mC. So: option 1 (Q0=27mC) is correct, option 2 (k=2) is correct, option 3 (9mC not 18mC) is wrong, option 4 (heat loss is not zero since charge redistributes). Wait options 1 AND 2 both look correct. For a single-answer context: the question is a multi-correct MCQ. Both options 1 (27 mC) and 2 (k=2) are correct.

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