### Video Transcript

An alternating current circuit contains a resistance of 125 ohms, an inductor with a 450-ohm inductive reactance, and a capacitor with a 28-ohm capacitive reactance. What is the impedance of the circuit? Give your answer to the nearest ohm.

Let’s start by looking at a sketch of the circuit we’re working with. We’re told this is an alternating current circuit that has a resistor, an inductor, and a capacitor. If we call 𝑅 the circuit resistance, we’re told that that is 125 ohms. Next, though, notice that it’s not the inductance and the capacitance of these components that we’re given. Instead, it’s something called their reactance. There is the inductive reactance 𝑋 sub L and the capacitive reactance 𝑋 sub C. Reactance is similar to resistance. We can see that because the units of reactance are ohms, just like resistance.

Knowing all this, we want to calculate what’s called the impedance of the circuit. Impedance is represented by a capital 𝑍. It’s an overall measure of a circuit’s opposition to the flow of charge. Impedance includes the reactance of any component in the circuit as well as the total resistance. Impedance is given by this equation. It’s the square root of the total resistance 𝑅 of the circuit squared plus the quantity 𝑋 sub L, the inductive reactance, minus 𝑋 sub C, the capacitive reactance, squared. Note that we’re given all three of these values for our circuit, so we can calculate its impedance.

Substituting in for 𝑅, 𝑋 sub L, and 𝑋 sub C, we get this expression. Entering this on our calculator, if we round our answer to the nearest whole number, we get 440. And note that the units of impedance are ohms, just like resistance and reactance. The overall opposition of this circuit to the flow of charge, that is, its impedance, is 440 ohms.