Topic: Network Theory
What is the value of C such that equivalent capacitance across X-Y is 5 F?
- A. 20 F
- B. 23 F
- C. 22 F
- D. 21 F
Answer: D. 21 F
Explanation: By applying star to delta conversion repeatedly as shown in the source diagrams, the network simplifies to an equivalent capacitance $C_{eq} = \frac{19}{8} + \frac{3C}{3+C}$. Setting $C_{eq} = 5$ F, we get $5 = \frac{19}{8} + \frac{3C}{3+C} \Rightarrow \frac{3C}{3+C} = 2.625 \Rightarrow 3C = 7.875 + 2.625C \Rightarrow 0.375C = 7.875 \Rightarrow C = 21 F$.