AC Circuit Quiz #1

Suppose you have an air-core coil with inductance 200uH and resistance 0.09 ohms, connected in series with a 10 ohm resistor.

You apply a 15KHz 12 volt peak-to-peak sine wave across this series circuit.

What is the power dissipated in the coil?

What is the rms voltage measured across the coil?

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Are mentors elligible for the challenge? :stuck_out_tongue:

Sure. Interested students can learn by studying your answer.

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Let’s work exclusively with rms quantities: 12 Volts peak-to-peak is 6 Volts amplitude, and dividing by the square root of 2 (~ 1.41), we get an rms voltage of 4.24 V from the source.

At 15 kHz, the coil’s reactance is given by:

XL = omegaL = 2pifL = 2pi1510^3200*10^-6 = 18.85 ohms

The coil’s impedance, then

Zcoil = 0.09 + j*18.85

The circuit total impedance, considering the 10 ohm series resistor:

Ztotal = 10.09 + j*18.85

We can now determine the circuit’s total current, in magnitude:

|I| = |V|/|Z| = |4.24|/|10.09+j*18.85| = 4.24/21.38 = 0.198 A

The power dissipated in the coil, then, is due to its small resistance:

P = i^2 * R = 0.198^2 * 0.09 = 0.0035 = 3.5 mW

We can determine the voltage drop in the coil using a voltage divider:

Vcoil = Vsource * Zcoil/Ztotal = 4.24*(0.09+j18.85)/(10.09+j18.85)
Vcoil = 3.3062+j*1.7495

The rms voltage that you would measure with a voltmeter is the magnitude of Vcoil:

|Vcoil| = |3.3062+j*1.7495|
|Vcoil| = 3.74 V

Nicely presented.

Students interested in AC circuit theory should carefully study your answer and ask questions if they need help understanding.

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I believe you meant 2pi15*10^3… not 10^-3. The math checks out otherwise.

Or am I just tired?

Matt

Yes, absolutely! The calculations are correct, I just typed it out wrong. :rolleyes:

Yep, I did the math out before I said anything, I get the same impedance as you, just a minor typo.

This was a fun challenge, any particular reason for it? It almost sounds like a motor controller to motor, if the wave was square instead of sine.

Just to raise awareness among interested students here on CD how AC calculations differ from the simple V=IR DC stuff they learned, and maybe motivate some to get into studying it.

It almost sounds like a motor controller to motor, if the wave was square instead of sine.

Yeah, it was inspired by some recent discussions here involving motor inductance and how that affects power calculations.

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AC power stuff is almost a form of black magic. :slight_smile:

Seriously though, it is pretty interesting, especially once you get in to reactance, systems can do weird things. I find students tend to get very interested in inductive backlash (which is what I call the tendency of inductive loads to cause interesting voltage fluctuations in an attempt to maintain current flow)

Eww math. I did too much of that today already, load calculations and voltage drops, motor conductor sizing, I slacked off on some bids and paperwork this week :rolleyes:

Students, while math is boring and you find it stupid (not that I blame you, no one really gives a darn where X is, it’s more fun when you can apply it and make money off it) it is important if you want a technical career.