Series RL circuit (Rev: 1.3)

Diagram 1: Inductor voltage (V_L) and current (I) waveforms


In a pure inductor, current flows across the inductor lags the inductor voltage (V_L) by 90 degree (diagram 1). In another words, inductor voltage (V_L) leads the current by 90 degree (diagram 1). This is because when the voltage is applied to an inductor, the back ElectroMotive Force (EMF) [Lenz's law] resists current build up in the inductor, causing the inductor current (I_L) to lag in time and phase than the inductor voltage (V_L). The reactance of an inductor (X_L) is the result of the inductor producing a back EMF which opposes change in the current.



Diagram 2: Series RL circuit (assume pure inductor)


Digital Storage Oscilloscope (DSO) measures and displays AC and DC voltages signals over a wide range of frequencies. DSO does not measures current. When using the DSO to plot the inductor voltage (V_L) and resistor voltage (V_R) on a series RL circuit (diagram 2) with a constant current, we can conclude the relationship of the phase of current to the inductor voltage (V_L) and resistor voltage (V_R) by using the phasor diagram.


Phasor diagram


Diagram 3: Phasor diagram of a series RL circuit (assume pure inductor)


According to Kirchoff's current law, the current at any given instant in a series circuit must be the same throughout all parts of the circuit. Therefore, total current (I_T) = resistor current (I_R) = inductor current (I_L) as shown in the phasor diagram (diagram 3) of a series RL circuit (diagram 2).

Since current is the only quantity which is common to all parts of a series circuit, it is used as a reference for zero phase (positive x-axis) to show the phase relationships between currents and voltages.

Since the resistor current (I_R) and resistor voltage (V_R) are in phase (zero phase), the resistor voltage (V_R) phasor will be on the same line on the positive x-axis. As the inductor voltage (V_L) leads the current by 90 degree (assume pure inductor), the inductor voltage phase is a positive 90 degree.


References:

[1] Phase relationships in AC circuits

[2] Wikipedia

[3] Basic electricity and electronics (By Charles A. Schuler and Richard J. Fowler)