AP EAMCET · PHYSICS · Capacitance

A parallel plate capacitor has a capacity \(80 \times 10^{-6} \mathrm{~F}\), when air is present between its plates. The space between the plates is filled with a dielectric slab of dielectric constant 20. The capacitor is now connected to a battery of \(30 \mathrm{~V}\) by wires. The dielectric slab is then removed. Then, the charge passing through the wire is

A \(12 \times 10^{-3} \mathrm{C}\)
B \(25.3 \times 10^{-3} \mathrm{C}\)
C \(120 \times 10^{-3} \mathrm{C}\)
D \(45.6 \times 10^{-3} \mathrm{C}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(45.6 \times 10^{-3} \mathrm{C}\)

Step-by-step Solution

Detailed explanation

\(C_{\text {air }}=80 \mu \mathrm{F}\) \[ C_{\text {dielectric }}=\varepsilon_r C_{\text {air }}=1600 \mu \mathrm{F} \] Charge stored in the presence of air, \[ q_{\text {air }}=C_{\text {air }} \times V=80 \times 30 \times 10^{-6}=2400 \mu \mathrm{C} \] Charge stored in…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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