MHT CET · Physics · Capacitance
In the given figure, the equivalent capacitance between points \(A\) and \(B\) is
- A \(1.5 \mathrm{C}\)
- B \(2 \mathrm{C}\)
- C \(3 \mathrm{C}\)
- D \(6 \mathrm{C}\)
Answer & Solution
Correct Answer
(A) \(1.5 \mathrm{C}\)
Step-by-step Solution
Detailed explanation
Both parts have capacitors in parallel. The equivalent capacitor for each part is \(\mathrm{C}_{\mathrm{eq}}=\mathrm{C}+\mathrm{C}+\mathrm{C}=3 \mathrm{C}\)
There are two \(3 \mathrm{C}\) capacitances in series
\(\therefore \quad \frac{1}{\mathrm{C}_{\mathrm{AB}}}=\frac{1}{3 \mathrm{C}}+\frac{1}{3 \mathrm{C}}\)
\(\frac{1}{C_{A B}}=\frac{2}{3 C}\)
\(\therefore \quad \mathrm{C}_{\mathrm{AB}}=1.5 \mathrm{C}\)
There are two \(3 \mathrm{C}\) capacitances in series
\(\therefore \quad \frac{1}{\mathrm{C}_{\mathrm{AB}}}=\frac{1}{3 \mathrm{C}}+\frac{1}{3 \mathrm{C}}\)
\(\frac{1}{C_{A B}}=\frac{2}{3 C}\)
\(\therefore \quad \mathrm{C}_{\mathrm{AB}}=1.5 \mathrm{C}\)
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