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Question

A parallel-plate capacitor has a dielectric slab in it. The slab just fills the space inside the capacitor. The capacitor is charged by a battery and then the battery is disconnected. Now, the slab is pulled out slowly at t=0. If at time t, the capacitance of the capacitor is C and potential difference between the plates of the capacitor is V, then which of the following graphs is/are correct.

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Solution

The correct options are

**A**

**C**

We need two relations one is between C and t and other is between V and t.

Let C be the capacitance with dielectric fully inserted.

Now the scenario is as shown

Ceq=Kε0(A−vtb)d+ε0vtbd

Ceq=Kε0Ad−Kε0vtbd+ε0vtbd=−t[Kε0vbd−ε0vbd]+Kε0Ad=−t[ε0vba[K−1]]+Kε0Ad

as the equation we obtained is in the form of y=−mx+c, option a is correct.

Again we have,

Q=CV

C=QV

C α 1V

Therefore option C is also correct.

We need two relations one is between C and t and other is between V and t.

Let C be the capacitance with dielectric fully inserted.

Now the scenario is as shown

Ceq=Kε0(A−vtb)d+ε0vtbd

Ceq=Kε0Ad−Kε0vtbd+ε0vtbd=−t[Kε0vbd−ε0vbd]+Kε0Ad=−t[ε0vba[K−1]]+Kε0Ad

as the equation we obtained is in the form of y=−mx+c, option a is correct.

Again we have,

Q=CV

C=QV

C α 1V

Therefore option C is also correct.

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