Question

A capacitor to be used in a radio is to have a reactance of \(6.20 \Omega\) at a frequency of \(520 \mathrm{Hz}\). What is the capacitance?

Short answer

Answer: The capacitance of the capacitor is 4.93 × 10^{-8} F.

Step-by-step solution

Write down the given values

We are given the reactance (\(X_C = 6.20 \Omega\)) and the frequency (\(f = 520 \mathrm{Hz}\)). Our goal is to find the capacitance (\(C\)).

Rearrange the formula for capacitance

Rearrange the formula for reactance in a capacitor to solve for capacitance: \(C = \frac{1}{2 \pi f X_C}\)

Plug the given values into the formula

Insert the given values for reactance and frequency into the rearranged formula: \(C = \frac{1}{2 \pi (520 \mathrm{Hz}) (6.20 \Omega)}\)

Solve for capacitance

Calculate the value of the capacitance: \(C = \frac{1}{2 \pi (520) (6.20)} = 4.93 \times 10^{-8} \mathrm{F}\) The capacitance of the capacitor is \(4.93 \times 10^{-8} \mathrm{F}\).