Question

what is the oscillation frequency of an LC circuit whose capacitor has a capacitance of $\mathbf{1}\mathit{\mu }\mathbf{\text{F}}$ and whose inductor has an inductance of $\mathbf{1}\mathbf{\text{mH}}$? (Both of these are fairly typical values for capacitors and inductors in electronic circuits. See Checkpoint 7 for a numerical example of inductance).

Short answer

The oscillating frequency of LC circuit is 5000 Hz.

Step-by-step solution

A concept:

The number of complete oscillations per unit of time commonly referred to as the oscillation frequency or frequency of oscillation

The given data:

Capacitance of the capacitor, $C=1\mu \text{F}=1\times {10}^{-6}\text{F}$

Inductance of the inductor,$L=1\text{mH}=1\times {10}^{-3}\text{H}$

The maximum voltage across the secondary coil:

The current in a pure LC circuit would oscillate sinusoidally. The energy would oscillate back and forth between the electric and magnetic, from the capacitor to the inductor and back again. The oscillating frequency of LC circuit is,

$f=\frac{1}{2\pi \sqrt{LC}}$

Substitute known values in the above equation.

$\begin{array}{c}f=\frac{1}{2\times 3.14\times \sqrt{\left(1\times {10}^{-3}\text{H}\right)\left(1\times {10}^{-6}\text{F}\right)}}\\ =\frac{1}{6.28\times 0.32\times {10}^{-4}}\\ =4976\text{Hz}\\ \approx 5000\text{Hz}\end{array}$

Hence, the oscillating frequency of LC circuit is$5000Hz$