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#1
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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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Re: AC Circuit Quiz #1
Are mentors elligible for the challenge?
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Re: AC Circuit Quiz #1
Sure. Interested students can learn by studying your answer.
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#4
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Re: AC Circuit Quiz #1
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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 Last edited by Manoel : 20-02-2011 at 19:23. Reason: small typo... kilo = 10^3, not 10^-3 |
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#5
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Re: AC Circuit Quiz #1
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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#6
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Re: AC Circuit Quiz #1
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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#7
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Re: AC Circuit Quiz #1
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#8
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Re: AC Circuit Quiz #1
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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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#9
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Re: AC Circuit Quiz #1
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.
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#10
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Re: AC Circuit Quiz #1
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![]() 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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#11
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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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