Engineering Electrical Engineering- Simple AC circuit problem

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In a series RL circuit connected to a 110-V AC source, the voltage across the resistor is 85 V, and the voltage across the inductor needs to be determined. The relationship between the voltages is expressed by the equation V_s^2 = V_r^2 + V_l^2, which is derived from the right triangle formed by the voltages, where V_s is the hypotenuse. The confusion arises from the understanding of the 110 V being the total voltage (hypotenuse) and the 85 V being the resistive voltage (one side of the triangle). The inductive reactance is at a right angle to the resistive voltage, which is why this triangle representation is applicable. Clarification on the phase relationship and the nature of these voltages is essential for solving the problem correctly.
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Homework Statement


I was able to find the solution to this problem but I don't understand where it comes from.

A series RL circuit is connect to a 110-V ac source. If the voltage across the resistor is 85 V, find voltage across inductor.



Homework Equations



Not sure.

The Attempt at a Solution



Solution is given as

V_s^2 = V_r^2 + V_l^2

then solve for V_l, I don't understand were that equation comes from or how it applies here. We are currently starting to learn how to solve circuits with the phasor method.
 
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The impedance of an inductor is called inductive reactance. It is called reactance to indicate that it is an imaginary number with no real part. (In reality all inductors have a small real part.) Because inductive reactance is at right angles to a resistor, the problem you are given amounts to a right triangle in which you are given the hypotenuse and one side. Now do you recognize the equation? The 110 VAC is the hypotenuse and the 85 VAC is the resistive voltage. Can you find the other side?
 
skeptic2 said:
The impedance of an inductor is called inductive reactance. It is called reactance to indicate that it is an imaginary number with no real part. (In reality all inductors have a small real part.) Because inductive reactance is at right angles to a resistor, the problem you are given amounts to a right triangle in which you are given the hypotenuse and one side. Now do you recognize the equation? The 110 VAC is the hypotenuse and the 85 VAC is the resistive voltage. Can you find the other side?

I understand they are at right angles to each other but I'm not sure why the hypotenuse is 110 V. Isn't the 110 V in phase with the V_r? so it points in the same direction as V_s? Isn't 85 V only the projects of the Voltage on the real axis and not the amplitude itself? What am I misunderstanding?
 
All set! For some reason the section that explained how that worked was the one after which this problem was presented.
 
Good
 

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