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