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$\bullet$ In an $R-L-C$ series circuit, $R=300 \Omega, L=0.400 \mathrm{H},$ and$C=6.00 \times 10^{-8} \mathrm{F}$ . When the ac source operates at the resonance frequency of the circuit, the current amplitude is 0.500 $\mathrm{A}$ . (a) What is the voltage amplitude of the source? (b) What is the amplitude of the voltage across the resistor, across the inductor, and across the capacitor? (c) What is the average power supplied by the source?

a) $V=1290 \mathrm{V}$b) $V=1290 \mathrm{V}$c) $P=37.5 \mathrm{W}$

Physics 102 Electricity and Magnetism

Chapter 22

Alternating Current

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

University of Michigan - Ann Arbor

University of Washington

Hope College

University of Sheffield

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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In an $L-R-C$ series circu…

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31.31. In an $L-R-C$ serie…

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An $L \cdot R-C$ series ci…

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An $L-R-C$ series circuit …

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for Burn A. We want people to gamble, too, and we're going to get that by setting illegal to I. Time's Olympians were eyes the current impotent since we're at Residences, the sequel to High are, since the impedance is equal to the resistance at residence, and now I can plug in the things we know. You know, the current apathy is 0.5 amps, and they are in The resistance is 300 homes. And so this gives 150 volts for being you. Yeah, for B, we need three things we need the voltage across resistant across the resistor, which is equal to, ay times a resistor. But that's just going to be this whole to cheer. So it's also won 50 bowls to figure out what the voltage is across the doctor In capacitor, we have to figure out what the react Ince's of those components are. So the reactions of the conductor is that legal, which is equal to L. A Times omega when we're at residence, which is one over square root of all times, have precedence. This is what omega is when we're at the resident frequency, which is what we're at this problem so clingy and everything. We'll get 2,580 tombs. And then now that we have, the reactions is we compare with the voltage is across the conductor. Let's go the current Appleton Times the reactant. And so this gives 1,290 volts. Same thing for the capacitor. This is equal to one over our legacy. But we know Omegas, and so this is just equal to the square root of L. A. Mercy if you're playing in one Omega's at residents and simplify the seas here. And so this gives 2,582 films. And so the voltage across faster physical Teo I times that react since And so this is 12 90 volts saying this up here and that completes part B for Percy. We want the average power. And so we're going to start with this formal here. Yeah, here fives the phase angle, and these are in the amplitude. And so we got current amplitude and bolted amplitude. And so let's use fee is equal to I R. So I'm just gonna plug in for V here, so get 1/2 r. I squared Time's coastline phase angle. And we know that this phase angle the coast I know that is equal to 11 We're at residents. So one if Omegas Omega knowledge and we are at residents. So just substituting one infer that co sign gives us this and the now Raina plug in values here and the sins of giving us 32 or 37 rather 37 and 1/2 watts, and that completes a problem.

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