Phase Difference between Voltage and Current

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SUMMARY

The discussion focuses on calculating the theoretical phase difference between current (CPA) and voltage (VPB) in a circuit with a 29-ohm resistor and an 11.1 mH inductor, driven by a 3.5 V sinusoidal voltage source. The relevant equation used is tan(x) = (XL / R), where XL is the inductive reactance calculated as (omega)(L). For a frequency of 20 Hz, the initial attempt yielded an incorrect phase angle of 2.75 degrees. The correct approach involves calculating the total impedance (Ztotal) and expressing both current and VPB in polar form to determine the phase difference accurately.

PREREQUISITES
  • Understanding of AC circuit analysis
  • Familiarity with inductive reactance (XL) and impedance (Z)
  • Knowledge of Ohm's Law
  • Ability to convert complex numbers to polar form
NEXT STEPS
  • Calculate the total impedance (Ztotal) for the given circuit
  • Learn how to derive the inductive reactance (XL) at different frequencies
  • Study the relationship between current and voltage phase angles in RLC circuits
  • Explore the use of phasors in AC circuit analysis
USEFUL FOR

Students in electrical engineering, particularly those studying AC circuits, as well as educators seeking to clarify concepts related to phase differences in inductive circuits.

Sylvia
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Homework Statement


screen_shot_2015-02-27_at_6.39.04_pm.png

The circuit above has a 29
omegacap.gif
resistor and a 11.1 mH inductor. Calculate the theoretical phase difference between the current CPA and voltage VPB if the circuit is driven by a sinusoidal voltage source with a peak amplitude of 3.5 V at the following frequencies:

20 Hz
420 Hz

Homework Equations


tan(x) = (XL / R), XL = (omega)(L)

3. The Attempt at a Solution

I tried substituting into the given relevant equations, and for 20 Hz, I got 2.75 degrees. However, this is the wrong answer. Please help!
 
Last edited by a moderator:
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Your relevant equation would give you the phase angle of the overall impedance, and that would in turn tell you the phase angle of the current with respect to the source voltage. But the question is asking you to compare the current's phase to that of the voltage across the inductor. You'll need to find expressions for the current and for VPB.
 
Last edited:
So current = 3.5 V divided by Ztotal, and VPb = I * L * omega?
 
Sylvia said:
So current = 3.5 V divided by Ztotal, and VPb = I * L * omega?
That's the idea. Don't forget the "j" in the inductor's impedance.
 
Im confused about where to proceed from there (my professor has done a horrible job of teaching this subject and the textbook isn't making much sense to me unfortunately)
 
Sylvia said:
Im confused about where to proceed from there (my professor has done a horrible job of teaching this subject and the textbook isn't making much sense to me unfortunately)
Calculate the current and the voltage VPB. Put the results in polar form (magnitude and phase angle).
 
Uhhhh sorry I'm in the non-calculus based class...
 
Sylvia said:
Uhhhh sorry I'm in the non-calculus based class...
? No calculus involved. Just circuit rules like Ohm's law.
 
Calculate the theoretical phase difference between the current CPA and voltage VPB
When you look at this closely, you can see that the question being asked is quite basic: what is the phase difference between current through an ideal inductor and the voltage across that ideal inductor.

No calculations are needed! :smile:

BTW, anyone know what is supposed to be represented by that box with a + and - on it??
 
  • #10
NascentOxygen said:
BTW, anyone know what is supposed to be represented by that box with a + and - on it??

Ammeter?
 

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