MHT CET · Physics · Capacitance
In the arrangement of the capacitors as shown in figure, each capacitor is of \(6 \mu \mathrm{F}\), then equivalent capacity between points \(\mathrm{A}\) and \(B\) is
- A \(12 \mu \mathrm{F}\)
- B \(6 \mu \mathrm{F}\)
- C \(4 \mu \mathrm{F}\)
- D \(10 \mu \mathrm{F}\)
Answer & Solution
Correct Answer
(D) \(10 \mu \mathrm{F}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{C}_1\) and \(\mathrm{C}_3\) are in parallel.
Hence their equivalent capacitance \(\mathrm{C}_5=2 \times 6=12 \mu \mathrm{F}\)
\(\mathrm{C}_5\) and \(\mathrm{C}_2\) in series. Hence their equivalent capacitance \(\mathrm{C}_6\) is given by
\(
\frac{1}{\mathrm{C}_6}=\frac{1}{12}+\frac{1}{6}=\frac{3}{12}=\frac{1}{4}
\)
\(\therefore \mathrm{C}_6\) and \(\mathrm{C}_4\) are in parallel.
Hence their equivalent capacitance is \(\mathrm{C}=4+6=10 \mu \mathrm{F}\)
Hence their equivalent capacitance \(\mathrm{C}_5=2 \times 6=12 \mu \mathrm{F}\)
\(\mathrm{C}_5\) and \(\mathrm{C}_2\) in series. Hence their equivalent capacitance \(\mathrm{C}_6\) is given by
\(
\frac{1}{\mathrm{C}_6}=\frac{1}{12}+\frac{1}{6}=\frac{3}{12}=\frac{1}{4}
\)
\(\therefore \mathrm{C}_6\) and \(\mathrm{C}_4\) are in parallel.
Hence their equivalent capacitance is \(\mathrm{C}=4+6=10 \mu \mathrm{F}\)
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