Understanding Faraday's Law: Investigating Phase Shift in an AC Circuit

Click For Summary

Discussion Overview

The discussion revolves around an experiment investigating Faraday's Law through the use of two solenoids in an AC circuit. Participants explore the phase shift between the electromotive force (emf) and the current, questioning the observed results and the underlying principles involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant describes an experiment with two solenoids, measuring the phase shift between emf and current, and notes a discrepancy in expected values.
  • Another participant inquires about the method used to measure the phase relation of current to voltage.
  • A participant explains the use of Loggerpro to graph the current and voltage, detailing the equations used to determine the phase difference.
  • Questions arise regarding the specifications of the solenoids, including their size, number of turns, and the frequency of the AC source.
  • One participant expresses a belief that the resistance of the coils may be influencing the phase shift, while also noting that the predicted results closely matched the actual results except for the phase discrepancy.
  • Another participant suggests that capacitive coupling between the coils, in addition to inductive coupling, could be affecting the phase shift, and mentions potential interference from power cables.
  • A later reply indicates uncertainty about the differential equations related to phase shifts and requests further assistance on the topic.

Areas of Agreement / Disagreement

Participants express differing views on the factors contributing to the unexpected phase shift, with some suggesting capacitive coupling and others focusing on resistance. The discussion remains unresolved regarding the exact causes of the observed discrepancies.

Contextual Notes

Participants mention various assumptions and conditions, such as the frequency of the AC source and the characteristics of the measuring instruments, which may influence the results but are not fully explored or resolved.

2.718281828459
Messages
9
Reaction score
0
I did an experiment with two solenoids, one inside the other. The inner solenoid was hooked up to an AC power source and ammeter. The outer coil had a voltmeter. This is a faraday's law experiment. Because the current is changing, we can find a formula for the emf. Here are my math steps:
View attachment untitled-1.pdf
So the phase shift for the emf minus the phase shift for the current should give pi/2, but it doesn't! The values I got were (1.103-1.977)=-0.874

What is going on?
 
Physics news on Phys.org
How did you measure the phase relation of current to voltage?
 
NascentOxygen said:
How did you measure the phase relation of current to voltage?

Loggerpro graphed both simultaneously (using a sin function for each). The general form for each equation was Asin(Bt+C)+D. I found C for each graph and then took the difference. Does that answer your question?
 
What size were the solenoids and how many turns? Was the excitation 60 Hz? What value (roughly) of voltage in the sensing coil did you experience?
 
I can give you all of the information I have if it will help, but conceptually the exact numbers shouldn't matter, right?

Yes, 60 Hz

number of turns of outer coil- (2920 pm 1)
number of turns of inner coil-(235 pm 1)
diameter of outer coil-(3.4200E-2 pm 7.8E-5) meters
diameter of inner coil- (1.7300E-2 pm 7.8E-5) meters
Length of inner coil- (12.000E-2 pm 7.8E-4) meters
Length of outer coil- (11.000E-2 pm 7.8E-4) meters

All 95% tri pdf

Emf max=2.270V

I also have values for the resistance, capacitance and inductance (from the manual, not from measurement)

Outer coil #29 wire, approx .29mm

Inductance: 63 pm 3 mH
Resistance 76 pm 2 Ω
Capacitance: 124 pm 2 pF

Inner coil #18 wire approx 1mm

Inductance: 78 pm 22 μH
Resistance: 0.4 pm 0.1 Ω
Capacitance: 142 pm 2 pF

I have a suspicion that this has to do with the resistance of the coils, but I still don't understand why or how the model I used is flawed. The predicted result was almost a perfect match with the actual result except for this shift.
 
diameter of outer coil-(3.4200E-2 pm 7.8E-5) meters
How many mm is that?

Anyway, my suggestion for the phase not being as expected hinges on there being capacitive coupling between the coils, in addition to the inductive coupling. Capacitive coupling gives a phase shift different from the transformer coupling. Added to this, there is always inductive coupling from power cables in the wall, and this may not have the same phase as the sinewave that is driving the solenoid here. The latter interference is more pronounced in high impedance circuits, and I surmise that the load on your sensing coil is the high input impedance of a voltmeter?
 
I'm still not getting this. Apparently there are some differential equations for this and the phase shift is frequency dependent. More help? Any idea what these equations are?
 

Similar threads

Graduate Faraday's law or Lorenzt force?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad AC Circuits Terminology: Phase shift vs Phase Angle
  • · Replies 3 ·
Replies
3
Views
10K
How to introduce a phase shift in an AC circuit
  • · Replies 17 ·
Replies
17
Views
7K
Graduate Parasitics in Solenoids: The Relationship Between AC Frequency and Induced EMF
  • · Replies 1 ·
Replies
1
Views
2K
Current in circular wire surrounding infinite solenoid in a circuit
  • · Replies 7 ·
Replies
7
Views
1K
Alternator torque when connected to a phase-shifted AC source
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How Does Faraday's Law Explain EMF Induction Outside a Solenoid?
  • · Replies 103 ·
4
Replies
103
Views
17K
Find maximum current in a coil using oscilloscopes and Faraday's Law?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Magnetic induction/ goal ref technology
  • · Replies 4 ·
Replies
4
Views
2K
Making sense of sequence of ideas in MIT OCW's 8.02 notes on Faraday
  • · Replies 1 ·
Replies
1
Views
2K