Video Transcript
An alternating voltage source with a frequency of 75 hertz is connected to a 35-millihenry inductor. What is the reactance of the circuit? Give your answer to two decimal places.
So, here is our circuit. It has an alternating voltage supply and an inductor. And we’re told that the frequency at which the voltage oscillates — we’ll call it 𝑓 — is 75 hertz and that the inductance of the inductor — we’ll call it 𝑙 — is 35 millihenries, thirty-five thousandth of a henry. Based on this, we want to know the reactance of the circuit. In general, reactance is similar to resistance. It has to do with how components in a circuit oppose the flow of electric charge. In our circuit, only one element has a meaningful reactance. That’s the inductor here. What we’re after then is the reactance represented by a capital 𝑋 of the inductor. If we solve for this, then we’ve solved for the reactance of the circuit.
To do this, we can recall that inductive reactance is defined as two 𝜋 times the frequency of oscillation of a circuit multiplied by its inductance. Since for our circuit we’re given both 𝑓 and 𝑙, we can substitute those values into our expression right away. Notice that in inserting the value for 𝑙, we’ve converted it from units of millihenries to units of henries. This is important for the sake of having consistent units across our expression.
The decimal equivalent of this value is 16.49336 and so on ohms. Since we want to give our answer to two decimal places, let’s look at the third number after the decimal, this three. Since three is less than five, when we round our answer to two decimal places, we won’t round up. The reactance of this circuit, specifically its inductive reactance, is 16.49 ohms.
