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Chapter 26: Problem 48

What capacitor in series with a \(100 \Omega\) resistor and a \(20 \mathrm{mH}\) inductor will give a resonance frequency of \(1000 \mathrm{Hz} ?\)

Short Answer

Expert verified
The required capacitor is \(2.00 nF\).

Step by step solution

01

Rearrange The Formula For Capacitance

We want to know the capacitance (C) to give the RLC circuit a proved resonance frequency, so we rearrange the resonance frequency formula for C:\[C = \frac{1}{4\pi^{2}f^{2}L}\]
02

Substitution

Substitute the given values into the formula, where \(L = 20mH = 20 \times 10^{-3} H\), \(f = 1000Hz\).\[C = \frac{1}{4\pi^{2}(1000)^{2} \cdot 20 \times 10^{-3}}\]
03

Calculation

Calculate the value of the capacitance:\[C = 2.00 \times 10^{-9} Farads\]So the required capacitance is \(2.00 \times 10^{-9} F\) or \(2.00 nF\).

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Most popular questions from this chapter

At what frequency \(f\) do a \(1.0 \mu \mathrm{F}\) capacitor and a \(1.0 \mu \mathrm{H}\) inductor have the same reactance? What is the value of the reactance at this frequency?

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