Inductance of a coil in an AC L-R circuit

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Homework Help Overview

The discussion revolves around the inductance of a coil in an AC L-R circuit, specifically examining the relationship between voltage, current, and phase angle in the absence of a capacitor. The original poster presents a question regarding the applicability of a specific formula for calculating the phase angle and inductance in a series circuit configuration.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the validity of using a formula that includes a capacitor when it is not present, and whether it can be simplified for a series L-R circuit. Some participants discuss the implications of series versus parallel configurations and the relevance of phase relationships in the context of the problem.

Discussion Status

The discussion is active, with participants exploring the conditions under which the formula applies and clarifying the assumptions about circuit configuration. There is a mix of agreement and caution regarding the application of the formula without a capacitor, indicating a productive exploration of the topic.

Contextual Notes

The original poster's question is framed within the context of a specific circuit setup involving a voltage source, an inductor, and a resistor, with a defined phase angle. There is an emphasis on understanding the role of components in the circuit and the implications of their arrangement.

ToxicBug
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Does the formula tan (phi) = (wL - 1/wC)/R work without a capacitor? Can I turn it into tan (phi) = wL/R instead? I don't know what formula to use to find the inductance of an inductor in this question:

A voltage source V = 160V sin (100t) is connected in series with an inductor and a 17.0 ohm resistor. The phase angle between the current and the voltage is 1.05 rad. Find:

a) the inductance of the coil, and
b) the average power consumption of a circuit.
 
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ToxicBug said:
Does the formula tan (phi) = (wL - 1/wC)/R work without a capacitor? Can I turn it into tan (phi) = wL/R instead?

Yes you can. The only reason it is wL-1/wC is because when a capacitor is present it's phasor is in the opposite direction due to the opposite phase difference it produces. That is, an inductor's voltage leads the current by 90 degrees while the capacitor's voltage lags the current by 90 degrees.
 
Careful!
You're adding Voltages here, so the formula only applies if the LCR is in *series*!
Not having a break in the wire where the capacitor used to be means V=0 there.
Sometimes devices are placed in parallel, and the formula does not apply.
 
yeah but he said it was in series.
 
I thought it would be helpful to give a couple of clues
as to why you don't set C=0 in that "formula".
 

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