How is total impedance calculated in an AC circuit with resistance and reactance?

Total impedance in an AC circuit is calculated using the formula Z = √(R² + X²) because it involves both resistance (R) and reactance (X). In an AC circuit, resistance contributes to the opposition to current flow, while reactance represents the opposition due to capacitance and inductance. These two components are not simply additive; rather, they are combined vectorially since they are perpendicular to each other in the complex plane.

In this context, resistance is a real part of the impedance that does not change with frequency, whereas reactance can change with frequency. By using the Pythagorean theorem, where the total impedance is the hypotenuse of a right triangle formed by resistance and reactance, the formula directly accounts for both elements’ contributions to the total impedance calculation. This approach results in a more accurate representation of how these components interact in alternating current scenarios.

Because the other proposed formulas either attempt to add or subtract the components linearly or use a division that does not apply to AC circuit analysis, they do not correctly represent the relationship between resistance and reactance in terms of total impedance.