The resistance in a series R-C circuit is 5 Ω. If the impedance of the circuit is 13 Ω, calculate the reactance of the capacitor
Question 1 Report
The resistance in a series R-C circuit is 5 Ω. If the impedance of the circuit is 13 Ω, calculate the reactance of the capacitor
Answer Details
In a series R-C circuit, the total impedance is given by:
Z = √(R^2 + Xc^2)
where R is the resistance and Xc is the reactance of the capacitor.
Since the impedance of the circuit is 13 Ω and the resistance is 5 Ω, we have:
13 = √(5^2 + Xc^2)
Squaring both sides, we get:
169 = 25 + Xc^2
Simplifying, we get:
Xc^2 = 144
Taking the square root of both sides, we get:
Xc = ±12
Since we are looking for the magnitude of the reactance, we take the positive value:
Xc = 12 Ω
Therefore, the reactance of the capacitor is 12 Ω.
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