Question

What is the resonant frequency of a $0.500mH$inductor connected to a$40.0\mu F$capacitor?

Short answer

The resonant frequency of a 0.500 mH inductor is 1.13kHz .

Step-by-step solution

Definition of inductor and capacitor

Capacitor: A capacitor is an electric charge storage device made up of one or more pairs of conductors separated by an insulator.

Indicator: An inductor is a component with inductance in an electric or electronic circuit.

Given data

The value of the inductor is$L=0.500mH\left(\frac{{10}^{-3}H}{1mH}\right)=5.00\times {10}^{-4}H$

The value of the capacitor is$C=40.0\mu F\left(\frac{{10}^{-6}H}{1\mu H}\right)=4.00\times {10}^{-5}F$

Finding the resonant frequency

Using the formula for an LC circuit, the resonant frequency can be expressed as,

$f_0=\frac{1}{2\pi \sqrt{LC}}$…………….(1)

Here, L is the self-inductance of the inductor and C is the capacitance.

Substituting the given values in equation (1), we get,

$$\begin{gathered} f_0=\frac{1}{2\times 3.14\times \sqrt{\left(5.00\times {10}^{-4}H\right)\left(4.00\times {10}^{-5}F\right)}} \\ =1.13\times \times {10}^{3}Hz\left(\frac{1kHz}{{10}^{3}Hz}\right) \\ =1.13kHz \end{gathered}$$

Therefore, the resonant frequency is$1.13kHz$