આકૃતિમાં દર્શાવેલ પરિપથમાં A અને B બિંદુ વચ્ચેનું સમતુલ્ય કેપેસિટન્સ કેટલું હશે ? અહીં પ્રત્યેક કેપેસિટરનું કેપેસિટન્સ \(C=3 \mu F\) છે.

A \(3 \mu F\)
B \(2 \mu F\)
C \(1 \mu F\)
D \(4 \mu F\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(2 \mu F\)

Step-by-step Solution

Detailed explanation

(B)
સમતુલ્ય પરિપથ

\(\begin{array}{l}C_{e q_1}=\frac{C}{2}+C+\frac{C}{2}=2 C \\ C_{e q_2}=\frac{C}{2}+\frac{C}{2}=C\end{array}\)
\(\Rightarrow\)\(C _{e q_1}\) અને \(C _{e q_2}\) ના શ્રેણી જોડાણનું સમતુલ્ય કેપેસિટન્સ
\(\begin{array}{l}C_{e q}=\frac{(2 C)(C)}{2 C+C}=\frac{2 C^2}{3 C} \\ C_{e q}=\frac{2 C}{3} \\ C_{e q}=\frac{2 \times 3}{3}=2 \mu F\end{array}\)

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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