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For the circuit in Figure $22.23, R=300 \Omega, L=0.500 \mathrm{H}$ and $C=0.600 \mu \mathrm{F}$ . The voltage amplitude of the source is 120 $\mathrm{V} .$ (a) What is the resonance frequency of the circuit? (b) Sketch the phasor diagram at the resonance frequency. (c) At the resonance frequency, what is the current amplitude through the source? (d) At the resonance frequency, what is the current amplitude through the resistor? Through the inductor? Through the branch containing the capacitor?

a) $=290.6 \mathrm{Hz}$b) See Graphc) 0.400 $\mathrm{A}$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Cornell University

Simon Fraser University

University of Winnipeg

McMaster University

Lectures

04:44

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug electrical appliances into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.

11:31

In electrical engineering, a direct current (DC) circuit is an electrical circuit operating with a constant voltage (or current), as opposed to alternating current (AC) circuits. Direct current may flow in a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams.

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$\bullet$ For the circuit …

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$\bullet$ In an $R-L-C$ se…

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$\bullet$ Consider the cir…

In an $L-R-C$ series circu…

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$\bullet$ In a series $R-L…

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In an L-R-C seriescirc…

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You have a 200-$\Omega$ re…

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An $L \cdot R-C$ series ci…

some party, eh? We want the resident frequency. And so to find this we're going to use the formula that don't make it on is you go to one more square it the induct inst times of precedents. And so now we can plug in what both these are, since they're both given in the problem and we get one point a three times 10 to the third radian per second. That's an angular frequency. So if we wanted a regular frequency, we would have to divide by two pi. And when we do that, we get 291 hurts. And so that's party and part of you want the phase or diagram. And so let's go ahead and draw our actual access here. What's their voltage goes off at some angle here? Well, at residence, we know that I's gonna be pointing in the same direction. So speedy FBI, We also know that I r is gonna be pointing in same direction, too. And then the other currents are perpendicular to this. So they're shooting off in this direction or destruction. So this is ill. The current cross the conductor, This is I C, and that's the face of a tiger. So here we want the current amplitude across the source. And so the equation. We're going to use this just Isaac Levy over the impedance. This is how you find the current amplitude, given the voltage, the opportunity and the impudence. But when we're at residents, we know the impedance is equal to the resistance. And so this stuff is because we're at residents and now we know what both these values are. And so this is 1 20 volts over 300 homes. And so this is 0.4 grams now, for part, even want the current amplitude across the resistor Thean doctor and the capacitor. And so let's start with the resistance, the current across the resistor it's just equal to the voltage or the resistance. But since we're at resident frequency, this is just going to be the same. Is this value and so is that. Now I need the current amplitude across the in doctor. And so that's just equal to the voltage over the reactions of the in doctor and the reactions of the doctor. It's just that you're frequency times thie induct in ce. And so now I comply in everything that we know and we know it all. So we can like that and get 0.131 amps. So it's a little less than these values here. You know, this one last time for the capacitor. In this case, it's volts over the reactions of the question playing what? The reactions, the capacitors, here's false omega precedents, and then playing in these values gives 0.131 amps, and so that completes the problem.

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