How is total impedance calculated in a RL circuit?

In a series RL circuit, the total impedance is calculated using the vector sum of resistance (R) and inductive reactance (XL). This relationship takes into account that resistance and reactance are perpendicular in the complex plane, which is why we use the Pythagorean theorem to calculate the magnitude of the total impedance.

The formula ( Z^2 = R^2 + XL^2 ) illustrates how the impedance (Z) is derived from its two components: resistance and reactance. By squaring the resistance and the reactance, summing those values, and then taking the square root of that sum, we find the total impedance. This accounts for both the real and imaginary components of the circuit, allowing for a comprehensive understanding of how they interact in electrical measurements.

This method does not apply to the other proposed methods, which either incorrectly combine these components or suggest a subtraction that does not accurately represent how impedance functions in a circuit. Thus, the selection of the quadratic formula for total impedance correctly captures the relationship between R and XL in an RL circuit.