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.