When voltage is applied to an RL circuit, what is the phase relationship between Er and Ir?

In an RL circuit, which consists of a resistor (R) and an inductor (L), the relationship between the voltage across the circuit (Er) and the current flowing through it (Ir) is a crucial aspect of understanding how these components behave in response to an alternating current (AC) voltage source.

When AC voltage is applied, the inductor causes a phase shift between the voltage and the current. Specifically, in an ideal scenario, the voltage across the resistor and the current through the circuit are in phase, meaning they reach their maximum and minimum values simultaneously. This is because the resistor does not introduce a phase shift; it follows Ohm's law, where voltage and current vary directly and proportionally.

In contrast, the inductor introduces a lagging phase shift to the current relative to the voltage. However, when we specifically consider Er and Ir, particularly across the resistor, we find that they are indeed in phase. Therefore, in the context of the resistor's voltage and current, the phase relationship is such that Er and Ir align in their peaks and troughs.

This understanding is foundational for analyzing AC circuits, particularly when determining impedance and phase angles in more complex scenarios. Recognizing the behavior of resistors and inductors