What is the result of vector addition in an AC circuit?

In the context of AC circuits, vector addition is essential for understanding the relationship between voltage, current, and impedance. When dealing with AC circuits, the values of voltage and current are often expressed as phasors, which are vectors that account for both the magnitude and phase angle of these quantities.

The correct result of vector addition in an AC circuit manifests as the total opposition to current flow, known as impedance. Impedance incorporates resistance and reactance (which can be inductive or capacitive), and it is represented as a complex number that reflects both the resistive and reactive components of the circuit. Through vector addition, these components are combined to determine the overall effect on current flow in the circuit.

In practical terms, if you only consider the resistive component (resistance, which does not change with frequency), you get the real part of impedance. The reactive components (inductive and capacitive reactance) contribute to the imaginary part. The interaction of these components leads to the total impedance, which, when vectorially added, gives a complete picture of how much opposition the current faces in the circuit. Understanding this total opposition is crucial for designing and analyzing electrical systems effectively.