**Concept:** 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 it's always going to be sinusoidal. Now because of that Ohms 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 times R cosine of Omega T. Right that is simply plugging in this equation into Ohms law very basic.

Let's do an example, a 10 resistor is plugged into and outlet with an R.M.S voltage of 120 volts, what is the maximum current in the circuit? What about the R.M.S. current? We know that the R M S voltage is 120 volts now just like we could say that the maximum current is equal to the maximum voltage over R it turns out that the R.M.S current is also equal to the R.M.S voltage divided by R. This something is really easy to show and you guys can convince that 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 R.M.S current So that's a square root of 2 times 12 amps which is about 17 amps resistors in AC circuits are very very simple problems. 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 to these circuits that have multiple resistors nothing changes from DC circuits. 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.

**Problem:** 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?

5m **Example:** Resistors in Parallel in an AC Circuit

Hey guys, let's do an example that involves multiple resistors and 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 the DC circuit but hold on just a second all of these elements are in parallel so they all share the voltage with the source 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'll call the maximum voltage across the 10 ohm resistor is just 5 volts which is the maximum voltage produced by the AC source. Now what does this mean about the maximum current through the 10 ohm resistor well by Ohms law I'll call I10 really quickly the maximum current through that 10 ohm resistor by Ohms 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? Didn't ask for the maximum current or the R.M.S current it just said the current so what we want to assume it means is the current as a function of time because the current doesn't have one particular value we have to list a current for all possible values of time all the possible values of current 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 currents 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.