What Determines Maximum Voltage in an RL Circuit with AC Power?

[XenoPhex]

I know this is a simple question but I can't quite figure out how to do this in a combined circuit:

Find the maximum voltage across a resistor R and inductor L with an AC power source of V₀sin(wt). (Note: the resistor is in series with the inductor) I'm trying to figure out the total max voltage and the max voltage for each (if that's even possible).

I'm a bit new to AC circuits so I don't really know how to handle things when dealing with them, so any extra tips outside of how to go about this problem would help immensely.

 

[vk6kro]

If you have an inductor and know its inductance you can work out its reactance at a known frequency by this formula:
XL = 2 * pi * F * L
eg 10000 hz and 1 mH, ZL =62.8 ohms

If this is put in series with a 100 ohm resistor, what would be the resulting impedance?

The easy way is to draw (or imagine) a triangle with R horizontal and XL vertically upward from the end of the resistive line (so it is a right angled triangle) and then draw a hypotenuse on these lines to make a triangle.
This hypotenuse represents the resultant impedance.

Using Pythagoras, Z^2 = R^2 + XL^2
so Z^2 = 100^2 + 62.8^2
from this Z= 118.08 ohms

So if you put 150 volts across the series combination at 10000 Hz the current would be
150 / 118.08 or 1.27 A

This current flows through the coil and the resistor.
Voltage across the resistor = I R = 1.27 * 100 = 127 V
Voltage across the coil = 1.27 * 62.8 = 79.76 V

Note that these add up to more than 150 volts, but their squares add up to the square of 150.