KCET · Physics · Capacitance

If a slab of insulating material (conceptual). \(4 \times 10^{-3} \mathrm{~m}\) thick is introduced between the plates of a parallel plate capacitor, the separation between the plates has to be increased by \(3.5 \times 10^{-3} \mathrm{~m}\) to restore the capacity to original value. The dielectric constant of the material will be

A 6
B 8
C 10
D 12

Verified Solution

Answer & Solution

Correct Answer

(B) 8

Step-by-step Solution

Detailed explanation

Let \(t\) be the thickness of the dielectric slab and \(K\) is the dielectric constant.
So, the increase in the distance of separation between the plates due to dielectric is given as
\(\begin{aligned}
x &=t-\frac{t}{K} \\
&=t\left(1-\frac{1}{k}\right)
\end{aligned}\)
Given, \(x=3.5 \times 10^{-3} \mathrm{~m}, t=4 \times 10^{-3} \mathrm{~m}\)
Substituting the given values in the above equation, we get
\(1-\frac{1}{k}=\frac{x}{t}=\frac{3.5 \times 10^{-3}}{4 \times 10^{-3}}=\frac{3.5}{4}\)
or
\(\frac{1}{k}=1-\frac{3.5}{4}=\frac{0.5}{4}\)
or
\(k=8\)

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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