Resistors in AC Circuits - Online Tutor, Practice Problems & Exam Prep

In AC circuits, the current is sinusoidal, and Ohm's law states that the voltage across a resistor is the product of current and resistance. The maximum voltage can be expressed as $I^{\max }=RI\left(t\right)$. For a 10-ohm resistor with an RMS voltage of 120 volts, the RMS current is 12 amps, and the maximum current is approximately 17 amps. Multiple resistors can be combined into an equivalent resistance for analysis.

Resistors in AC Circuits

Hey guys. In this video, we're going to start talking about resistors in AC circuits. Alright? Let's get to it. Just as a reminder, in an AC circuit, the current produced by the source is always going to look like this. Okay. It's always going to be sinusoidal. Alright. Now because of that, Ohm's Law tells us that the voltage across the resistor as a function of time has to be this current as a function of time times the resistance. Right? If we had a basic circuit exactly as above, the voltage across the resistor as a function of time would just be equal to the current traveling through it as a function of time times r the resistance. This means that the voltage across the resistor is Imax∗rcos⁡(ωt). Right? That is simply plugging in this equation into Ohm's Law. Very basic. Let's do an example. A 10 ohm resistor is plugged into an outlet with an RMS voltage of 120 volts. What is the maximum current in the circuit? What about the RMS current?

Okay. We know that the RMS voltage is 120 volts. Now just like we could say that current is equal to the maximum voltage over r, it turns out that the RMS current is also equal to the RMS voltage divided by r. This is something that's really easy to show and you guys can convince yourselves of that on your own. So, this is 120 volts divided by 10 ohms which is 12 amps. Now, what's the maximum current? Well, the maximum current is just going to be the square root of 2 times the RMS current. So that's the square root of 2 times 12 amps, which is about 17 amps. Okay? Resistors in AC circuits are very, very simple problems. Alright?

Now for multiple resistors in an AC circuit, what if you had something like this for instance? All we have to do is combine them into a single equivalent resistor as we would with DC circuits and then we can apply the same equations as we did in the previous example. Alright, guys. This was a little bit of a start with resistors in AC circuits and we'll get to more of that soon. Thanks for watching.

The voltage across a resistor is found to be given by v _R (t) = (10 V) cos[(120 s⁻¹)t]: 

a) At what frequency does the AC course operate? 

b) If the resistance is 12 Ω, what is the maximum current in this circuit? 

c) What is the RMS voltage of the AC source?

• A. a) 19.1 Hz;
  b) 0.83 A;
  c) 7.1 V
• B. a) 120 V;
  b) 1.2 A;
  c) 2.2 V
• C. a) 754 Hz;
  b) 120 A;
  c) 14 V

Resistors in Parallel in an AC Circuit

Hey guys, let's do an example that involves multiple resistors in an AC circuit. What is the current through the 10 ohm resistor in the following circuit? Now your first instinct might be to just jump right in and start combining resistors like you would in a DC circuit, but hold on just a second. All of these elements are in parallel, so they all share the voltage with the source. Okay? So the maximum voltage across each of these resistors is the same as the maximum voltage across the AC source.

So, we can say v10, which I will call the maximum voltage across the 10 ohm resistor, is just 5 volts, which is the maximum voltage produced by the AC source. Okay. Now, what does this mean about the maximum current through the 10 ohm resistor? Well, by Ohm's Law, I'll call i10 really quickly, the current through that 10 ohm resistor. By Ohm's Law, that's just going to be the maximum voltage divided by the resistance. So that's going to be 5 volts, which is the maximum voltage, divided by 10 ohms. So, this is going to be half an amp. Now, the question says what is the current? It didn't ask for the maximum current or the RMS current. It just said the current. So what we want to assume it means is the current as a function of time. Okay?

Because the current doesn't have one particular value, we have to list the current for all possible values of time, all of the possible values of current. Okay? So the current as a function of time, we know is just going to be the maximum current times cosine of omega t. So what we need to know is the maximum current and omega. We know that the maximum current through the 10 ohm resistor is half an amp and we know that the angular frequency is 200 inverse seconds. So this is just going to be 0.5 amps times cosine of 200 inverse seconds times time, and this is the current at any point in time through that 10 ohm resistor. Alright, guys, thanks for watching.