# Max Voltage in an RL Circuit

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.

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