A capactior with no dielectric between its plates is connected in series with a

Question

A capactior with no dielectric between its plates is connected in series with a resistor and a battery and allowed to acquire the maximum possible charge for this set up. With the capacitor fully charged and the battery still connected to the circuit, a dielectric is inserted between the plates of the capacitor (assume instantaneously) and the circuit remains connected in this set up for a very long time thereafter (assume infinite time).

If Qc is the charge on the capacitor and Vc the potential drop across its plates, then which of the following statements is true for Qc and Vc after the dielectric is inserted as compared to the case without the dielectric?

A. Qc increases but Vc decreases.

B. Qc decreases but Vc increases.

C. Qc increases but Vc remains the same.

D. Qc decreases but Vc remains the same.

E. Qc remains the samebut Vc increases.

F. Qc remains the samebut Vc decreases.

G. Both Qc and Vc increase.

H. Both Qc and Vc decrease.

I know the answer is C, but I don't know why. An explanation of why it is C is enough.

Explanation / Answer

When Dielectric is inserted , Capacitance increases.

Inittial Capacitance, C = A*eo/d
Final Capacitance, C' = k*Aeo/d (k is the dielectric constant)

The battery acts as an external agent which pumps charge onto the plates in order to maintain the potential difference. As it is attched to the same battery during the insertion of the dielectric, Voltage drop would be constant and remain the same, i.e Vc remains the same.

Now, Qc = C'*Vc
As C' > C , Therefore Qc' > Qc.

So Charge increases,

Correct Option - (C)

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