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Chapter 23: Q95PE (page 863)

What is the resonant frequency of a 0.500mHinductor connected to a40.0μFcapacitor?

Short Answer

Expert verified

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

Step by step solution

01

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.

02

Given data

The value of the inductor isL=0.500mH10-3H1mH=5.00×10-4H

The value of the capacitor isC=40.0μF10-6H1μH=4.00×10-5F

03

Finding the resonant frequency

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

f0=12πLC…………….(1)

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

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

f0=12×3.14×5.00×10-4H4.00×10-5F=1.13××103Hz1kHz103Hz=1.13kHz

Therefore, the resonant frequency is1.13kHz

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Most popular questions from this chapter

The \(4.00{\rm{ }}A\) current through a \(7.50{\rm{ }}mH\) inductor is switched off in \(8.33{\rm{ }}ms\). What is the emf induced opposing this?

What is the peak emf generated by rotating a 1000-turn, \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{ T}}\) diameter coil in the Earth’s magnetic field, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in \({\rm{10}}{\rm{.0 ms}}\)?

Camera flashes charge a capacitor to high voltage by switching the current through an inductor on and off rapidly. In what time must the \(0.100{\rm{ }}A\) current through a \(2.00{\rm{ }}mH\) inductor be switched on or off to induce a \(500{\rm{ }}V\) emf?

Consider the use of an inductor in series with a computer operating on 60 Hzelectricity. Construct a problem in which you calculate the relative reduction in voltage of incoming high-frequency noise compared to 60 Hzvoltage. Among the things to consider are the acceptable series reactance of the inductor for 60 Hzpower and the likely frequencies of noise coming through the power lines.

(a) Find the current through a\(0.500{\rm{ }}H\)inductor connected to a\(60.0{\rm{ }}Hz,{\rm{ }}480{\rm{ }}V\)AC source. (b) What would the current be at\(100{\rm{ }}kHz\)?
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