MHT CET · Physics · Capacitance

In a parallel plate air capacitor the distance between plates is reduced to one fourth and the space between them is filled with a dielectric medium of constant 2. If the initial capacity of the capacitor is $4 μ F .$ then its new capacity is

A $32 μ F$
B $18 μ F$
C $8 μ F$
D $44 μ F$

Verified Solution

Answer & Solution

Correct Answer

(A) $32 μ F$

Step-by-step Solution

Detailed explanation

The capacitance of a parallel plate air capacitor is given by

C_{0} = \frac{ε_{0} A}{d}

Where,

ε_{0}

=permittivity of the medium,
A = area of plates
and d = distance between the plates
When the distance between plates is reduced and a dielectric slab is introduced, then the capacitance becomes

C = \frac{K ε_{0} A}{d_{1}}

… (ii)
Where, K = dielectric constant of medium.
Here, K = 2,

d_{1} = \frac{d}{4}

and

C_{0} = 4 μ F

4 \times 10^{- 6} F

From Eq. (ii), we get

C = 4 (\frac{K ε_{0} A}{d_{1}}) = 4 K (\frac{ε_{0} A}{d})

= 4 K C_{0}

…. (iii) [From Eq. (i)]
Substituting given values in Eq. (iii), we get

C = 4 \times 2 \times 4 = 32 μ F

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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In a parallel plate air capacitor the distance between plates is reduced to one fourth and the space between them is filled with a dielectric medium of constant 2. If the initial capacity of the capacitor is 4μF. then its new capacity is

Step-by-step Solution

In a parallel plate air capacitor the distance between plates is reduced to one fourth and the space between them is filled with a dielectric medium of constant 2. If the initial capacity of the capacitor is $4 μ F .$ then its new capacity is