Phase Angle between Voltage and Current

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SUMMARY

The discussion centers on calculating the phase angle between voltage and current in an AC circuit involving a resistor and an inductor. The impedance of the series combination was calculated to be 389.94 ohms. The phase angle can be determined using the formula ɸ = cos⁻¹(R/Z) or ɸ = tan⁻¹(XL/R). The user initially struggled with finding the inductive reactance (XL) but later realized the necessary formulas for calculating both XL and the phase angle.

PREREQUISITES
  • Understanding of AC circuit theory
  • Familiarity with Ohm's Law
  • Knowledge of impedance and reactance
  • Ability to use trigonometric functions in electrical calculations
NEXT STEPS
  • Learn how to calculate inductive reactance (XL) using the formula XL = 2πfL
  • Study the relationship between impedance (Z), resistance (R), and reactance (X)
  • Explore the concept of phasors in AC circuit analysis
  • Investigate the effects of frequency on impedance in R-L circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in AC circuit analysis will benefit from this discussion.

theintarnets
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Homework Statement



"When only a resistor is connected across the terminals of an ac generator (111 V) that has a fixed frequency, there is a current of 0.465 A in the resistor. When only an inductor is connected across the terminals of this same generator, there is a current of 0.360 A in the inductor. When both the resistor and the inductor are connected in series between the terminals of this generator, calculate the following.
(a) the impedance of the series combination


(b) the phase angle between the current and the voltage of the generator"

I got the impedance to be 389.94, but I don't know what other formulas to use to get the phase angle. Specifically, I don't know how to find XL.


Homework Equations



Phase angle = arctan(XL/R)
 
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Nvm, I found another formula for phase angle = cos(R/Z)

I had the wrong variables written into the equation of Z, so I didn't realize I already calculated XL >.<
 
Last edited:
I don't know how to find XL.

How would you find R? It is similar.
 
theintarnets said:
Nvm, I found another formula for phase angle = cos(R/Z) ✗[/size][/color]

phase angle ɸ = cos⁻¹ (R/Z)

this is identical with ɸ = tan⁻¹ (X/R)
 
barryj said:
I don't know how to find XL.

How would you find R? It is similar.
Ohm's Law, you know the applied voltage and you know the current that flows.
 

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