Video Transcript
An alternating-voltage source with a frequency of 50 hertz is connected to a 125-microfarad capacitor. What is the reactance of the capacitor? Give your answer to the nearest ohm.
Let’s say that this is our alternating-voltage source. It has a frequency of 50 hertz, and it’s part of a circuit that includes a capacitor. The capacitance of the capacitor is 125 microfarads. Knowing all this, we want to solve for what’s called the reactance of the capacitor. Symbolized 𝑋 sub 𝑐, reactance is a measure of how much a component opposes the flow of charge. It’s not quite the same thing as resistance, but it’s related. We see that from the fact that the units of reactance are ohms, just like those of resistance.
These three quantities — capacitive reactance, capacitance, and the frequency of our circuit — are related by a mathematical expression. That expression defines the reactance of a capacitor as one over two 𝜋 times the frequency of oscillation in the circuit multiplied by its capacitance. In our case, since we know 𝑓 and we know 𝐶, we can substitute those values into our equation. Note that we’ve converted our capacitance from units of microfarads to farads.
When we calculate this expression, we get a result of 25.4647 dot dot dot and so on and so forth ohms. We’ll report our answer though rounded to the nearest ohm. Therefore, we say that the reactance of the capacitor is 25 ohms.
