A capacitor of \(2.0 \times 10^{-11 F }\) and an inductor are joined in series. The value of the inductance that will give the circuit a resonant frequency of \(200 kHz\) is ____________
A. \(\frac{1}{16} H\) B. \(\frac{1}{8} H\) C. \(\frac{1}{64} H\) D. \(\frac{1}{32} H\)
Correct Answer: D
Explanation
\begin{aligned} &\text { At resonance } \\ &X_{L}=X_{C} \\ &2 \pi f L=\frac{1}{2 \pi \times f C} ; L=\frac{1}{2 \pi^{2} f^{2} C} \\ &L=\frac{1}{4 \times 3.142^{2} \times\left(2 \times 10^{2}\right)^{2} \times 2 \times 10^{-11}} \\ &L=0.031=\frac{1}{32} H \end{aligned}
