You have a 200-Ω resistor, a 0.400-H inductor, and a 6.00-μF capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. (a) What is the impedance of the circuit?

Video transcript

Welcome back everybody. We are making observations about an L R circuit here and we are called a couple of different things. It is connected to a power source that has a measured 120 volts and a frequency of 60 Hertz connected in series to a Resistor with a resistance of 15 omegas and an induct er with an inductive of .3 hertz. And we are tasked with finding what the impedance is of our l our circuit. Luckily, we have a formula for this for an LR circuit. The impedance is calculated by R squared plus our inductive reactant squared. But what is our inductive reactant? Well, this is just simply going to be equal to our induction. Uh Let's see here times our angular frequency, but we don't have an angular frequency. So this is just going to be our induct incense times two pi times our frequency. Let's go ahead and plug this into our formula here and then solve. So we have Z L R is equal to the square root of 15 squared plus, we have our inductive of 150.3 times two times pi times R frequency of 60 Hertz and all of that will be squared. When you plug this into our calculator, we get 114.1 Omegas for the impedance corresponding to our final answer. Choice of C Thank you all so much for watching. Hope this video helped. We will see you all in the next one.