How to calculate a series RL circuit without losing your mind

Ok so here’s the situation:

Your parents are away on a weeks vacation and….. They left you with an AC series RL circuit to figure out.

They are back tomorrow, you’ve spent all the grocery money on pizza and beer and you haven’t even started to work on the problem.

Basically you’re screwed.

Until now. I am here to help.

This tutorial is going to break the circuit down into easy to follow steps as well as provide you with a video walkthrough of the entire circuit.

Step one: Calculate impedance.

RL circuit, inductor, resistor

In order to make any progress in this circuit you need to turn your inductance into a reactance.

Using the formula 2πfl = XL we can determine that a 300 mH inductor at 60 hz will have a reactance of 113 Ω.

Now we have something we can work with. We can go ahead and build an impedance triangle.

We need to do this to determine the circuit current as the current is determined by the impedance of a circuit not its resistance.

impedance triangleAre you getting excited yet? I know I am!

Step two: Determine circuit current.

Now that we have an impedance (total opposition to current flow) we have the key that unlocks everything.

We use the circuit voltage and divide it by the circuit impedance and we can determine the circuit current.

120 V / 151 Ω = .795 Amps

RL3

Step three: Determine voltages.

I guess we should figure out some voltages.

Now that we have current, resistances, reactance and an impedance it is easy breezy.

The only tricky part to the whole thing is the voltage across the coil.

It is important for us to remember that a coil contains inductance and resistance. This means that we have to calculate for the impedance of the coil alone.

RL4

Now all we have to do is solve using ohms law for the voltages.

I X R = the resistor voltage.

I X Z (coil) = the coil voltage.

RL5

Step 4: Determine power.

Well it is almost over. Thank goodness.

The only thing left to calculate are the powers.

We can go ahead and use the formulas:

I²R = W
I²XL = Vars
I²Z = VA

RL6

Step 5:Party like it’s 1999

Crack a cold one because you are done son!

Remember to take the time to break it down into steps and you should have no problem.

Make sure to watch the video as I go through it in a step by step process.

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