Calculating voltage division for an AC circuit?

[159753x]

Homework Statement

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

Homework Equations

V = IR

The Attempt at a Solution

How does one go about solving this? My intuition tells me that KVL must be satisfied. Therefore, wouldn't the voltage drop just be 110 - 85 = 25V?

The answer key states that the answer is 69.82 V.

Instead of explaining how to get the solution, can someone perhaps explain how Kirchoff's Voltage Law is different in AC circuits then DC? I can't quite understand why my logic above doesn't work, and the answer isn't 25V.

 

[Bystander]

V = IR

Ohm's law, DC only.

different in AC circuits then DC?

Current through an inductor lags voltage across the inductor by 90 degrees (or pi/2 radians) in AC circuits. Current through a resistor is in phase (zero lag or lead) in AC circuits. Current through a capacitor leads voltage by 90 or pi/2. Check your textbook index or appendices for "reactance." Try this and see if it helps.

 

[159753x]

I got it! The total voltage coming from the AC source varies with time, so the voltage across the resistor also varies with time. Once I realized that this voltage of 110V is really the length of a vector in the complex plane, it becomes much easier. Obviously, if the voltage of the resistor is only 85V, the inductor must carry the rest of the voltage (here we use the pythagorean theorem). Thus 85^2 - 110^2 = 69.8^2 .

Thanks for the help!