Calculate the value of capacitance in picofarad, which will make … - Vidyadip

Question

Calculate the value of capacitance in picofarad, which will make 101.4 micro henry inductance to oscillate with frequency of one megahertz.

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Answer

Data $: f _{ r }=10^6 Hz , L =101.4 \times 10^{-6} H$
$
f_{ r }=\frac{1}{2 \pi \sqrt{L C}} \quad \therefore f_{ r }^2=\frac{1}{4 \pi^2 L C}
$
$
\begin{aligned}
& \therefore C=\frac{1}{4 \pi^2 f_r^2 L}=\frac{1}{4(3.142)^2\left(10^6\right)^2\left(101.4 \times 10^{-6}\right)} \\
= & \frac{10000 \times 10^{-10}}{4(3.142)^2(101.4)}=2.497 \times 10^{-10} F \\
= & 249.7 \times 10^{-12} F =249.7 \text { picofarad }
\end{aligned}
$
This is the value of the capacity.

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