KCET · Physics · Capacitance
All capacitors used in the diagram are identical and each is of capacitance C. Then the effective capacitance between the point \(A\) and \(B\) is
- A \(1.5 \mathrm{C}\)
- B \(6 \mathrm{C}\)
- C \(\mathrm{C}\)
- D 3C
Answer & Solution
Correct Answer
(A) \(1.5 \mathrm{C}\)
Step-by-step Solution
Detailed explanation
The equivalent diagram of the given circuit is
\(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) are in parallel
\(\therefore \mathrm{C}_{123} =\mathrm{C}_{1}+\mathrm{C}_{2}+\mathrm{C}_{3} \)
\(=\mathrm{C}+\mathrm{C}+\mathrm{C}=3 \mathrm{C}\)
Similarly, \(C_{456}=3 C\)
\(\mathrm{C}_{123}\) and \(\mathrm{C}_{456}\) are in series
\(\therefore C_{\text {eq }}=\frac{(3 C)(3 C)}{3 C+3 C}=1.5 C\)
\(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) are in parallel
\(\therefore \mathrm{C}_{123} =\mathrm{C}_{1}+\mathrm{C}_{2}+\mathrm{C}_{3} \)
\(=\mathrm{C}+\mathrm{C}+\mathrm{C}=3 \mathrm{C}\)
Similarly, \(C_{456}=3 C\)
\(\mathrm{C}_{123}\) and \(\mathrm{C}_{456}\) are in series
\(\therefore C_{\text {eq }}=\frac{(3 C)(3 C)}{3 C+3 C}=1.5 C\)
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