Answer:
[tex]3.8\times 10^{-8}\ H[/tex]
Explanation:
Given the [tex]6.7\mu F[/tex] capacitor is used in an LC circuit to produce [tex]10\ kHz[/tex] frequency.
We need to find the value of inductance required.
As we know the relation between angular frequency in [tex]rad/sec[/tex] and frequency in [tex]Hz[/tex] is.
[tex]\omega =2\times \pi\times f[/tex]
Where [tex]\omega[/tex] is angular frequency and [tex]f[/tex] is frequency.
[tex]\omega=2\times \pi\times 10\times 1000=20000\pi\ rad/sec\\\omega=62832\ rad/sec[/tex]
Also, the relation between the angular frequency, capacitance and inductance is given by.
[tex]\omega^2=\frac{1}{LC}\\\\L=\frac{1}{\omega^2C} \\\\L=\frac{1}{62832^2\times6.7\times 10^{-6} } \\\\L=\frac{1}{26451}.\\ \\L=3.8\times 10^{-8}\ H[/tex]
So, [tex]3.8\times 10^{-8}\ H[/tex] inductance will be required to produce [tex]10\ kHz[/tex].
