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Chapter 36: Problem 26

What inductor in series with a \(100 \Omega\) resistor and a \(2.5 \mu \mathrm{F}\) capacitor will give a resonance frequency of \(1000 \mathrm{Hz} ?\)

Short Answer

Expert verified
The value of the inductor is 0.01 Henrys or 10 mH.

Step by step solution

01

Understand the formula

The formula to calculate the resonance frequency \(f\) in a series RLC circuit is \(f = \frac{1}{2 \pi \sqrt{LC}}\), where L is the inductance in Henrys, C is the capacitance in Farads. Here, we are given the values of \(f, C\) and we need to solve for \(L\). Firstly, convert all the values to basic units. Therefore, \(f = 1000 \, Hz\), C= \(2.5 \times 10^{-6} \, F \( .
02

Rearranging the formula to solve for the inductor

Rearrange the formula to get \(L\), the inductance: \(L = \frac{1}{(2 \pi f)^2 \times C}\).
03

Plug in the values

Substitute the known values into the equation: \(L = \frac{1}{(2 \pi \times 1000)^2 \times 2.5 \times 10^{-6}}\).
04

Calculate the value

Perform the calculations to find the value of \(L\). After doing so, we find that \(L = 0.01H\), or in other terms, \(10 mH\).

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Most popular questions from this chapter

A low-pass filter consists of a \(100 \mu \mathrm{F}\) capacitor in series with a \(159 \Omega\) resistor. The circuit is driven by an AC source with a peak voltage of \(5.00 \mathrm{V}\) a. What is the crossover frequency \(f_{c} ?\) b. What is \(V_{\mathrm{C}}\) when \(f=\frac{1}{2} f_{\mathrm{c}}, f_{\mathrm{c}},\) and \(2 f_{\mathrm{c}} ?\)

\(\mathrm{A} 0.30 \mu \mathrm{F}\) capacitor is connected across an AC generator that produces a peak voltage of \(10 \mathrm{V}\). What is the peak current to and from the capacitor if the emf frequency is (a) \(100 \mathrm{Hz} ?\) (b) 100 kHz?

A resistor dissipates \(2.0 \mathrm{W}\) when the rms voltage of the emf is 10.0 V. At what rms voltage will the resistor dissipate \(10.0 \mathrm{W} ?\)

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

A series RLC circuit attached to a \(120 \mathrm{V} / 60 \mathrm{Hz}\) power line draws 2.4 A of current with a power factor of \(0.87 .\) What is the value of the resistor?
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