In summary, the conversation discusses the calculation of the theoretical phase difference between the current and voltage in a circuit with a 29 resistor and an 11.1 mH inductor driven by a sinusoidal voltage source at 20 Hz and 420 Hz. The relevant equation for finding the phase angle of the overall impedance is tan(x) = (XL / R), with XL = (omega)(L). However, this equation does not provide the phase angle between the current and voltage across the inductor. To find this, the current and voltage VPB must be calculated and put in polar form, with no calculus involved. The circuit includes an ammeter.
  • #1
Sylvia
30
1

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!
 
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  • #2
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.
 
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  • #3
So current = 3.5 V divided by Ztotal, and VPb = I * L * omega?
 
  • #4
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.
 
  • #5
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)
 
  • #6
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).
 
  • #7
Uhhhh sorry I'm in the non-calculus based class...
 
  • #8
Sylvia said:
Uhhhh sorry I'm in the non-calculus based class...
? No calculus involved. Just circuit rules like Ohm's law.
 
  • #9
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?
 

Related to Phase Difference between Voltage and Current

1. What is phase difference between voltage and current?

The phase difference between voltage and current refers to the difference in timing between the two waveforms. It is measured in degrees and represents the delay between the peak of the voltage waveform and the peak of the current waveform.

2. Why is phase difference between voltage and current important?

The phase difference between voltage and current is important because it affects the power factor of an electrical system. A high power factor means that the voltage and current are in phase, resulting in efficient energy transfer. A low power factor, on the other hand, means that the voltage and current are out of phase, leading to energy loss and potential damage to electrical equipment.

3. How is phase difference between voltage and current measured?

The phase difference between voltage and current is measured using an oscilloscope or a power analyzer. These instruments can display the two waveforms and calculate the phase difference in degrees.

4. What causes phase difference between voltage and current?

There are several factors that can cause phase difference between voltage and current. These include inductive and capacitive loads, which create a lag or lead between voltage and current respectively. Other factors include the length and type of electrical wiring, as well as the type of electrical equipment being used.

5. How can phase difference between voltage and current be corrected?

Phase difference between voltage and current can be corrected by using power factor correction techniques. This involves adding capacitors or inductors to the electrical system to counteract the effects of inductive or capacitive loads. Another way to correct phase difference is by using active power factor correction devices, which continuously monitor and adjust the power factor to maintain efficiency.

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