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GUJCET · Physics · Electrostatic Potential and Capacitance
As shown in below circuit, the effective capacitance is _________ \(\mu F\).
- A 4
- B 1
- C \(\frac{30}{11}\)
- D \(\frac{8}{11}\)
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
(A)
equivalent capacitance of series connections of
\(C _2\) and \(C _3\)
\(\begin{array}{ll} & \frac{1}{ C ^{\prime}}=\frac{1}{ C _2}+\frac{1}{ C _3} \\ \therefore & \frac{1}{ C ^{\prime}}=\frac{1}{6}+\frac{1}{3} \\ \therefore & \frac{1}{ C ^{\prime}}=\frac{3}{6}=\frac{1}{2} \\ \therefore & C ^{\prime}=2 \mu F\end{array}\)
equivalent capacitance of parallel connection of
\(\begin{array}{l}C_1 \text { and } C^{\prime} \\ C=C_1+C^{\prime} \\ C=2+2 \\ C=4 \mu F\end{array}\)
equivalent capacitance of series connections of
\(C _2\) and \(C _3\)
\(\begin{array}{ll} & \frac{1}{ C ^{\prime}}=\frac{1}{ C _2}+\frac{1}{ C _3} \\ \therefore & \frac{1}{ C ^{\prime}}=\frac{1}{6}+\frac{1}{3} \\ \therefore & \frac{1}{ C ^{\prime}}=\frac{3}{6}=\frac{1}{2} \\ \therefore & C ^{\prime}=2 \mu F\end{array}\)
equivalent capacitance of parallel connection of
\(\begin{array}{l}C_1 \text { and } C^{\prime} \\ C=C_1+C^{\prime} \\ C=2+2 \\ C=4 \mu F\end{array}\)
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