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An $L-R-C$ series circuit consists of a source with voltage amplitude 120 V and angular frequency 50.0 rad/s, a resistor with R = 400 $\Omega$, an inductor with $L$ = 3.00 H, and a capacitorwith capacitance $C$. (a) For what value of C will the current amplitude in the circuit be a maximum? (b) When $C$ has the value calculated in part (a), what is the amplitude of the voltage across the inductor?

(a) $1.33 \times 10^{-4} \mathrm{F}=133 \mu \mathrm{F}$(b) $45.0 \mathrm{V}$

Physics 102 Electricity and Magnetism

Chapter 31

Alternating Current

Section 5

Resonance in Alternating-Current Circuits

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

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.

07:19

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".

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welcome to the golden number thirty one point three zero. This is thirty one alternating current. So in this question, were given a faulty circuit. So we have R confessions and an inductive. This's any sizzles. This has working temp actually calls to one twenty walls and this is over l which is three hundred. This is our r, which is four hundred on and this is our confessions, but you don't know and we have the is his source which has an F frequency pickles to fifty million per second. So in first. But we need to find out the and pictures of the current and we need to find out the condition. And what is the will of the capacitance in that condition, which makes the imperial current maximum. So if you look in there for me off the current attitude, so we have paper. So our eye is the current temperature, which is, of course, to the world is amplitude over impotence. Now this is over imprudent. So if we look at the formula carefully to maximize thie current value, we have combat minimize this valley, and this can be only minimized if XY is a coast too. Except this is the minimum. Or this is the condition which maximizes the current and minimizes the agenda. So this is a real condition, which means there isn't a frequency, resin and condition, which means we have X e which is because to one or Omega Psi should because we excel, which is a cause Tau Omega. So this gives us omega equals to one over Elsie. But we know Omega. We know else we can find out. That's C here. So we have sequels too. One over Omega Square supporting all this way we have fifty radian per second. Amina taking the square times end which is three hundred disconcert to B one point territory in the bandits or minus four. I said, honey, so this is the capacitance of the capacitor. Now the next step is to find out the current. So we have we well done a picture over our This gives us current now looking at this one so that it becomes because X is over equals to accent. Therefore, this becomes well looking at it. So we have I now we have because one twenty one r is over four hundred. This gives us point three m Pierre. Now, this is the current amplitude. Now we need to find out the wordage amplitude across in dr which is I x l because tu ai o me o l. So which is point three times fifty radian per second. James three handed. So this concert to be forty five words. So that's over. Answer for this question. Thank you. For what? In the video.

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