Topic: Network Theory
10 $\mu\text{F}$ capacitor is connected across secondary winding of a high frequency transformer having primary to secondary turns ratio 5:2. What is the value of capacitance seen across primary?
- A. $4~\mu\text{F}$
- B. $62.5~\mu\text{F}$
- C. $25~\mu\text{F}$
- D. $1.6~\mu\text{F}$
Answer: D. $1.6~\mu\text{F}$
Explanation: For a transformer, the reflected impedance is $Z_{1} = Z_{2}\left(\frac{N_{1}}{N_{2}}\right)^{2}$. Since $Z = \frac{1}{j\omega C}$, this implies $C_{1} = C_{2}\left(\frac{N_{2}}{N_{1}}\right)^{2}$.
Given $C_2 = 10~\mu\text{F}$ and $\frac{N_1}{N_2} = \frac{5}{2}$, we have $C_{1} = 10 \times 10^{-6}\left(\frac{2}{5}\right)^{2} = 10 \times 10^{-6} \times \frac{4}{25} = 1.6~\mu\text{F}$.