AP EAMCET · PHYSICS · Capacitance

A parallel plate capacitor has plates of area \(0.4 \pi \mathrm{~m}^2\) and spacing of 0.5 mm. If a slab of thickness 0.5 mm and dielectric constant 4.5 is introduced in between the plates of the capacitor, then the capacitance of the capacitor is

A 100 nF
B 60 pF
C 100 pF
D 60 nF

Verified Solution

Answer & Solution

Correct Answer

(A) 100 nF

Step-by-step Solution

Detailed explanation

\( C = \frac{k \epsilon_0 A}{d} \) \( C = \frac{4.5 \times 8.854 \times 10^{-12} \, \mathrm{F/m} \times 0.4 \pi \, \mathrm{m}^2}{0.5 \times 10^{-3} \, \mathrm{m}} \) \( C \approx 100 \times 10^{-9} \, \mathrm{F} = 100 \, \mathrm{nF} \)

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.

Same subject

Explore more questions on app

From AP EAMCET

Explore more questions on app