આકૃતિમાં બતાવ્યા પ્રમાણે, \(200\,cm ^2\) સમાન પ્લેટનું ક્ષેત્રફળ ધરાવતા બે સમાંતર પ્લેટ કેપેસિટરને એવી રીતે જોડાયેલા છે કે \(a \neq b\). સંયોજનનું સમતુલ્ય કેપેસીટન્સ \(x \varepsilon_0 F\) છે. \(x\) ની કિંમત ................ છે.

A \(4\)
B \(3\)
C \(5\)
D \(2\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(5\)

Step-by-step Solution

Detailed explanation

\(c=\frac{\varepsilon_0 A}{(d-c)}\) \(=\frac{\varepsilon_0 \times 200 \times 10^{-4}}{4 \times 10^{-3}}\) \(\therefore x=5\) The situation is equivalent to a conducting slab placed between the plates

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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