In a purely resistive circuit with alternating voltage, how do voltage and current behave?

In a purely resistive circuit, the behavior of voltage and current is such that they are in phase with each other. This means that when the voltage reaches its peak value, the current also reaches its peak value at the same time, and the same is true for the zero crossing points in their waveforms.

This in-phase relationship occurs because resistors do not introduce any phase shift between voltage and current. The relationship can be understood through Ohm's law, which states that voltage (V) equals current (I) times resistance (R). Since there is no reactive component (like inductance or capacitance) in a purely resistive circuit, there is no phase difference introduced; hence, the voltage and current rise and fall together.

Understanding this concept is critical for analyzing AC circuits effectively, as knowing that voltage and current are in phase helps in calculating power and understanding how energy is consumed in resistive loads. In contrast, in circuits with inductors or capacitors, voltage and current do not behave in this synchronous manner due to phase shifts introduced by the reactive components.