Question

What inductance do you need to produce a resonant frequency of \(60.0{\rm{ }}Hz\), when using a \(3.52{\rm{ }}H\) capacitor?

Short answer

The inductance we need to produce a resonant frequency of \(60.0{\rm{ }}Hz\) when using an \(2.00\mu H\) capacitor is \(3.52H\).

Step-by-step solution

Definition of inductor and capacitor

A capacitor is a device that stores electric charge and is composed of one or more pairs of conductors and an insulator.

In a circuit for electricity or electronic devices, an inductor is a component with inductance.

Given Information

The resonant frequency value is:\(60.0{\rm{ }}Hz\)

The capacitance value is: \(3.52{\rm{ }}H\)

Formula used

Using the formula for an LC circuit, the resonant frequency

\(\begin{aligned} {f_0} &= \frac{1}{{2\pi \sqrt {lC} }}\\ \Rightarrow C &= \frac{1}{{4{\pi ^2}l{f^2}_b}}\end{aligned}\)

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

Inductance we need to produces a resonant frequency

We have\(C = 2.00 \times {10^{ - 6}}\;F\) and\({f_0} = 60\;Hz\)

Substituting the given values in above equation,

we get,

\(\begin{aligned} L &= \frac{1}{{4 \times 3.14 \times 2 \times {{10}^{ - 6}} \times {{(60)}^2}}}\\ \Rightarrow L &= 3.52H\end{aligned}\)

Therefore, the required inductance is \(3.52H\).