Question

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. \( \frac{7}{10} \, \mu F \)

Hint:

For capacitors:
- In \textbf{series}, the reciprocal of the total capacitance is the sum of reciprocals: \[ \frac{1}{C_{\text{eq}}} = \sum \frac{1}{C_i} \]
- In \textbf{parallel}, the total capacitance is simply the sum: \[ C_{\text{eq}} = \sum C_i \]