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JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
In the circuit shown, find \(C\) if the effective capacitance of the whole circuit is to be \(0.5\,\mu F.\) All values in the circuit are in \(\mu F.\)
- A \(\frac{7}{{11}}\mu F\)
- B \(\frac{6}{{5}}\mu F\)
- C \(4\,\mu F\)
- D \(\frac{7}{{10}}\mu F\)
Answer & Solution
Correct Answer
(A) \(\frac{7}{{11}}\mu F\)
Step-by-step Solution
Detailed explanation
\(\mathrm{C}_{\mathrm{eq}}=0.5\, \mu \mathrm{F}=\frac{\left(1+\frac{4}{3}\right) \mathrm{C}}{\frac{7}{3}+\mathrm{C}}=\frac{7 \mathrm{C}}{\frac{7}{3}+\mathrm{C}}=\frac{1}{2}\) \(\Rightarrow \quad \frac{14 \mathrm{C}}{3}=\mathrm{C}+\frac{7}{3}\) \(C=\frac{7}{11}\)
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