Complex Impedance: Time-domain Expression for i(t) w/ Measured R & L

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The discussion focuses on deriving the time-domain expression for current i(t) based on measured resistance (R) and inductance (L) values in an AC circuit. The calculations involve complex impedance, leading to the expression i(t) = 0.263cos(2000∏t + 77°), but confusion arises regarding the relationship between voltage and current in the presence of an inductor. Participants highlight the importance of consistency in using peak or peak-to-peak values for voltage in calculations, as discrepancies in measured values are noted. Suggestions are made to remeasure values in the lab to ensure accuracy, especially since the instructor is new to teaching the course. The conversation emphasizes the need for clarity in understanding AC circuit behavior and the application of Ohm's law to complex circuits.
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Homework Statement


Time-domain expression for i(t), based on measures above:
Time-domain expression for i(t), based on measured R and L:

Vp-p on 16Ω resistor: 7.25mV "measured above"
Ip-p for resistor: 0.676mA "measure above"
Ip for resistor: .338mA "measured above"

R: 14.8Ω L: 10.1mH "measured R and L"

Source voltage is 5Vp-p 0 off-set at 1kHz

Homework Equations


? The issue is that I need to make the equations I suppose.

The Attempt at a Solution


This is for the measured R and L values:

Ip = Vp/(R + jωL) = 2.5/(14.8 + j2000∏*10.1) = 2.5/(14.8 + j63.5) = 37/622 - j(159/622) = 59E-3 - j256E-3

i(t) = R(cosωt - β)

R = √(x2 + y2) = √((59E-3)2 + ((256E-3)2) = 263E-3

β = tan-1(-256/59) = -77°

i(t) = 0.263cos(2000∏t + 77°)

Some specific issues:
1. How in the world can i(t) = Rcos(ωt - β)? Wouldn't that make voltage lag current which shouldn't happen when an inductor is in the circuit?

2. When I do the problem with
Vp-p on 16Ω resistor: 7.25mV "measured above"
Ip-p for resistor: 0.676mA "measure above"
Ip for resistor: .338mA "measured above"
should I be using Vp = 7.25E-3/2 or Vp = Vsource p-p/2? The instructions in the lab manual and the slides from the professor that wrote the manual where not clear.

Thanks in advance!
 
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Is there a particular circuit configuration that we should know about? :smile:
 
gneill said:
Is there a particular circuit configuration that we should know about? :smile:

Lol I'm not sure, but here it is:

circuit2.jpg


PS, this is an intro-lab if that wasn't obvious enough. lol
 
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BuddhaBelly34 said:

Homework Statement


Time-domain expression for i(t), based on measures above:
Time-domain expression for i(t), based on measured R and L:

Vp-p on 16Ω resistor: 7.25mV "measured above"
Ip-p for resistor: 0.676mA "measure above"
Ip for resistor: .338mA "measured above"

R: 14.8Ω L: 10.1mH "measured R and L"

Source voltage is 5Vp-p 0 off-set at 1kHz

Homework Equations


? The issue is that I need to make the equations I suppose.


The Attempt at a Solution


This is for the measured R and L values:

Ip-p = Vp/(R + jωL) = 2.5/(14.8 + j2000∏*10.1) = 2.5/(14.8 + j63.5) = 37/622 - j(159/622) = 59E-3 - j256E-3
You don't want to mix p-p and p quantities. Choose one "type" for your computations and stick to it.

Something misfired in your complex number calcs above; The result looks off.

Also, if I go by the 5Vpp @1KHz source and the given component values, the magnitude of the current that I calculate would be about 77 mA p-p, or 38 mA peak. So something is fishy about your "measured above" values or the component values.
i(t) = R(cosωt - β)

R = √(x2 + y2) = √((59E-3)2 + ((256E-3)2) = 263E-3

β = tan-1(-256/59) = -77°

i(t) = 0.263cos(2000∏t + 77°)

Some specific issues:
1. How in the world can i(t) = Rcos(ωt - β)? Wouldn't that make current voltage lag current which shouldn't happen when an inductor is in the circuit?
What's a "current voltage"?
2. When I do the problem with
Vp-p on 16Ω resistor: 7.25mV "measured above"
Ip-p for resistor: 0.676mA "measure above"
Ip for resistor: .338mA "measured above"
should I be using Vp = 7.25E-3/2 or Vp = Vsource p-p/2? The instructions in the lab manual and the slides from the professor that wrote the manual where not clear.
Well, it depends upon what it is you're trying to calculate. Make a clear statement of what it is you're trying to determine. If it's the magnitude of the current flowing through the resistor, then Ip = Vp/R, or Ipp = Vpp/R, where both Vp and Vpp are measured across R.
 
Edited my post, I didn't mean "current voltage" I was typing "voltage lag current" but added a current in front of voltage.

As for picking "p-p" or "p" it was just a type-o going to fix that too.

"Also, if I go by the 5Vpp @1KHz source and the given component values, the magnitude of the current that I calculate would be about 77 mA p-p, or 38 mA peak. So something is fishy about your "measured above" values or the component values."
This is something that I, unfortunately, cannot fix. This is my professor's first time teaching this class, so there is more self teaching than anything and I probably made some mistakes with the oscilloscope (which is basically push buttons and hope you get it right :( ).

"Something misfired in your complex number calcs above; The result looks off. " Like rounding errors? Or something in the algebra? I was rounding as I was going.
 
"Well, it depends upon what it is you're trying to calculate. Make a clear statement of what it is you're trying to determine. If it's the magnitude of the current flowing through the resistor, then Ip = Vp/R, or Ipp = Vpp/R, where both Vp and Vpp are measured across R."

I'm assuming it's Ip because the lab manual says "... i(t) = Ipcos(wt-b)".
 
BuddhaBelly34 said:
"Something misfired in your complex number calcs above; The result looks off. " Like rounding errors? Or something in the algebra? I was rounding as I was going.

$$\frac{2.5\;V}{14.8 + 63.46j \; \Omega} \cdot \frac{14.8 - 63.46j}{14.8 - 63.46j} → \frac{37 - 158.65j}{4246}\;A = 8.71 + 37.36j \; mA $$
 
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edit since there is no delete.
 
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okay I found my mistake. this guy in my class keeps changing my ti-83's notation to eng from normal and i miss the E's half the time. I get what you get now (now being paying attention to the Es lol)

So if the measured values look wrong should I go into the lab and remeasure?

Okie doke, phase angle stays the same but now I have R = 0.0387. :P
 
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  • #10
BuddhaBelly34 said:
okay I found my mistake. this guy in my class keeps changing my ti-83's notation to eng from normal and i miss the E's half the time. I get what you get now (now being paying attention to the Es lol)

So if the measured values look wrong should I go into the lab and remeasure?

That might not be a bad idea. You might want to determine at least the order of magnitudes to expect for the values. Also confirm the part values and supply frequency. If you have an Ohmmeter handy, check to see if the inductor has a non-negligible resistance.

When using an oscilloscope, always check to see if any scope probe you're using has a scaling factor associated with it (quite often they divide by ten).

For the current that you measured, what type of instrument did you use? Was it an ammeter? Does it provide values in peak or RMS? (typically they present RMS values assuming a sinusoidal signal).

Supposing that R = 14.8 Ω, L = 10.1 mH, and f = 1 KHz, then what do you think you should see for the voltage across the resistor?
 
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  • #11
gneill said:
That might not be a bad idea. You might want to determine at least the order of magnitudes to expect for the values. Also confirm the part values and supply frequency. If you have an Ohmmeter handy, check to see if the inductor has a non-negligible resistance.

When using an oscilloscope, always check to see if any scope probe you're using has a scaling factor associated with it (quite often they divide by ten).

For the current that you measured, what type of instrument did you use? Was it an ammeter? Does it provide values in peak or RMS? (typically they present RMS values assuming a sinusoidal signal).

Supposing that R = 14.8 Ω, L = 10.1 mH, and f = 1 KHz, then what do you think you should see for the voltage across the resistor?

I thought that I was supposed to calculate the current? http://utdallas.edu/~dodge/EE1202/lab5.pdf Top of page 7.

Not sure what I should be seeing across the resistor. I don't understand AC circuits that well. Since it is in series the voltage across the resistor and the inductor must equal the source voltage right? So VL + VR = VS. I think VL = IXL where XL = wL.
 
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  • #12
BuddhaBelly34 said:
I thought that I was supposed to use the oscilloscope to measure the current? http://utdallas.edu/~dodge/EE1202/lab5.pdf Top of page 7. I figured it was the amplitude of the current trace.

Ah. From the caption on the figure there: "The 'current' trace is really resistor voltage, but it is in phase with the current."

So the actual (p-p) current would be given by that curve's p-p voltage divided by the resistance.
 
  • #13
Yeah that is why I made the edit. Sorry, too much going on in my head right now. I had that problem first last night then the professor corrected me. Assuming my lab partner took the right reading for voltage on the resistor I have V = 7.25mV.

Ip = Vp-p/2R = 244.9E-6 A
 
  • #14
BuddhaBelly34 said:
Not sure what I should be seeing across the resistor. I don't understand AC circuits that well. Since it is in series the voltage across the resistor and the inductor must equal the source voltage right? So VL + VR = VS. I think VL = IXL where XL = wL.

You can treat the impedance of the inductor just as you would a resistance as far as the usual circuit equations are concerned. The only difference is that you'll be dealing with complex values in the calculations.

Your two components (resistor, inductor) are going to behave like a voltage divider. So if E is the input voltage and R and ZL the impedances of the parts, what voltage should you expect across the R?
 
  • #15
I'm not sure. Sorry for being ignorant, but there was no "intro to EE" class before this lab course. So I'm learning as I go.
 
  • #16
If you can calculate the (complex) current, then you can determine the (complex) voltages for the individual components via Ohm's law. Their magnitudes should match those of the traces you see on the scope.
 

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