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23 Nov 2019

Write at least a paragraph in which you derive the equationfor the volage across an inductor in an AC circuit.

Discuss the frequency dependence of XL.

Discuss what happens to the current in an RL circuit as thefrequency changes.

How does this compare to the way the current charges as afunction of frequency in an RC circuit?

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31.28. An L-R-C series circuit is constructed using a 175-22 resistor, a 12.5-F capacitor, and an 8.00-mH inductor, all con- nected across an ac source having a variable frequency and a voltage amplitude of 25.0 V. (a) At what angular frequency will the impedance be smallest, and what is the impedance at this fre- quency? (b) At the angular frequency in part (a), what is the maxi- mum current through the inductor? (c) At the angular frequency in part (a), find the potential difference across the ac source, the resistor, the capacitor, and the inductor at the instant that the cur- rent is equal to one-half its greatest positive value. (d) In part (c), how are the potential differences across the resistor, inductor, and capacitor related to the potential difference across the ac source?

find the amplitude of the current i0 through the voltage source.

To understand the use of phasors in analyzing a parallel AC circuit.Phasor diagrams, or simply phasors, provide a convenient graphical way of representing the quantities that change with time along with .This makes them useful for analyzing AC circuits with their inherent phase shifts between voltage and current. If a quantity I(t) changes with time as , a phasor is a vector whose length represents the amplitude Io(see the diagram). This vector is assumed to rotate counterclockwise with angular speed ; that way, the horizontal component of the vector represents the actual value I(t) at any given moment.In this problem, you will use the phasor approach to analyze an AC circuit.

In answering the questions of this problem, keep the following in mind.

For a resistor, the current and the voltage are always in phase.

For an inductor, the current lags the voltage by .

For a capacitor, the current leads the voltage by .

Part A

Phasors are helpful in determining the values of current and voltage in complex AC circuits.

Consider this phasor diagram:

The diagram describes a circuit that contains two elements connected in parallel to an AC source. The vector labeled corresponds to the voltage across both elements of the circuit. Based on the diagram, what elements can the circuit contain?

1) two resistors

2) two inductors

3) two capacitors

4) a capacitor and a resistor

5) an inductor and a resistor

6) a capacitor and an inductor

Part B

Find the amplitude

of the current through the voltage source.

Express your answer in terms of the magnitudes of the individual currents

fuchsialocust876

Hi, I just need help with the last part of this problem. Ifigured out how to work parts a & b, and I am now stuck on howto get part c.

Here's the whole question:

An AC power supply with a maximum potential of 45 V is across aseries RLC circuit, where the inductance is 15 mH, the capacitanceis 94 nF, the resistance is 17 Î©.

a) Find the resonant frequency. Answer in units of kHz.
(I got 4.239kHz)

b) Find the amplitude of the current at the resonantfrequency.
(The answer is 2.647 A)

This is the part I am stuck on:

c) Find the amplitude of the voltage across the inductor atresonance.
Answer in units of V.

Thank you!

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