TS EAMCET · Physics · Capacitance

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , the capacitance is \(C_1\). If one third of the space between the plates of the capacitor is filled with the medium of dielectric constant 4 , the capacitance is \(C_2\). If in both cases, the dielectric is placed parallel to the plate of the capacitor, then \(C_1: C_2=\)

A \(2: 3\)
B \(4: 3\)
C \(6: 5\)
D \(7: 5\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(6: 5\)

Step-by-step Solution

Detailed explanation

Capacitance of capacitor when dielectric of thickness t and dielectric constant \(K\) is placed between plates \(C=\frac{\epsilon_0 A}{d-t+\frac{t}{K}}\) In first case. \(C_1=\frac{\epsilon_0 A}{d-d / 2+\frac{d}{8}}=\frac{8 \epsilon_0 A}{5 d}\) In second case…

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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