Linemen Institute Practice Test

Impedance in AC circuits combines resistance and reactance as two perpendicular components. In complex form, Z = R + jX, where R is the resistance and X is the reactance. The magnitude of impedance, which is what Z represents when talking about its size or how it impedes current, is found with the Pythagorean relation |Z| = sqrt(R^2 + X^2). This comes from treating the resistive part and the reactive part as orthogonal directions in the complex plane, so you square, add, and take the square root. For example, if R = 3 ohms and X = 4 ohms, the impedance magnitude is 5 ohms. The sign of X affects the phase angle (phi = arctan(X/R)) but not the magnitude, since X is squared in the formula. The other forms don’t give the true magnitude: simply adding R and X ignores the 90-degree phase difference between resistance and reactance, while multiplying or subtracting them does not represent how these components combine directionally in the impedance.