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Unread 20-02-2011, 17:08
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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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Unread 20-02-2011, 17:14
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Re: AC Circuit Quiz #1

Are mentors elligible for the challenge?
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Unread 20-02-2011, 17:19
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Re: AC Circuit Quiz #1

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Originally Posted by Manoel View Post
Are mentors elligible for the challenge?
Sure. Interested students can learn by studying your answer.


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Unread 20-02-2011, 17:53
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Re: AC Circuit Quiz #1

Quote:
Originally Posted by Ether View Post


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?

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 = omega*L = 2*pi*f*L = 2*pi*15*10^3*200*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+j*18.85)/(10.09+j*18.85)
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
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Last edited by Manoel : 20-02-2011 at 19:23. Reason: small typo... kilo = 10^3, not 10^-3
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Unread 20-02-2011, 18:03
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Re: AC Circuit Quiz #1

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Originally Posted by Manoel View Post
...
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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Unread 20-02-2011, 18:51
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Re: AC Circuit Quiz #1

Quote:
Originally Posted by Manoel View Post
XL = omega*L = 2*pi*f*L = 2*pi*15*10^-3*200*10^-6 = 18.85 ohms
I believe you meant 2*pi*15*10^3.... not 10^-3. The math checks out otherwise.

Or am I just tired?

Matt
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Unread 20-02-2011, 19:21
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Re: AC Circuit Quiz #1

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Originally Posted by Matt Krass View Post
I believe you meant 2*pi*15*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.
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Unread 20-02-2011, 19:34
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Re: AC Circuit Quiz #1

Quote:
Originally Posted by Manoel View Post
Yes, absolutely! The calculations are correct, I just typed it out wrong.
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.
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Unread 20-02-2011, 20:04
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Re: AC Circuit Quiz #1

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Originally Posted by Matt Krass View Post
This was a fun challenge, any particular reason for it?
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.


Quote:
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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Unread 20-02-2011, 20:14
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Re: AC Circuit Quiz #1

Quote:
Originally Posted by Ether View Post
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.
AC power stuff is almost a form of black magic.

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)
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Unread 21-02-2011, 02:50
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Re: AC Circuit Quiz #1

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


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.
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