In an R-L parallel circuit, if IR is the current through pure resistor and IL is the current through pure inductor, then phase relation between IR and IL is:

Explanation:

Phase Relation in R-L Parallel Circuit

Definition: In an R-L parallel circuit, a resistor (R) and an inductor (L) are connected in parallel to each other across an AC supply. The current through the resistor (I_R) and the current through the inductor (I_L) are the main components to consider for analyzing the phase relationship.

Phase Relationship: The phase relationship between the current through the resistor (I_R) and the current through the inductor (I_L) is a fundamental concept in AC circuit analysis. In an AC circuit containing a resistor and an inductor in parallel:

• The current through the resistor (I_R) is in phase with the voltage across the resistor.
• The current through the inductor (I_L) lags the voltage across the inductor by 90 degrees.

This means that I_R is in phase with the supply voltage (V), and I_L lags the supply voltage (V) by 90 degrees. Therefore, the phase difference between the current through the resistor (I_R) and the current through the inductor (I_L) is 90 degrees.

Correct Option Analysis:

The correct option is:

Option 3: 90 degrees

This option correctly describes the phase relationship between the current through the resistor (I_R) and the current through the inductor (I_L) in an R-L parallel circuit. The current through the inductor lags the current through the resistor by 90 degrees.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 0 degrees

This option is incorrect because if the phase difference was 0 degrees, it would imply that the currents through both the resistor and the inductor are in phase with each other and the supply voltage. However, in an R-L parallel circuit, the current through the inductor always lags the supply voltage by 90 degrees, so the phase difference cannot be 0 degrees.

Option 2: 45 degrees

This option is incorrect because a 45-degree phase difference would imply that the current through the inductor lags the current through the resistor by 45 degrees. However, in an R-L parallel circuit, the phase difference between I_R and I_L is specifically 90 degrees, not 45 degrees.

Option 4: 180 degrees

This option is incorrect because a 180-degree phase difference would imply that the current through the inductor is completely out of phase with the current through the resistor. However, in an R-L parallel circuit, the current through the inductor lags the current through the resistor by 90 degrees, not 180 degrees.

Conclusion:

Understanding the phase relationship in an R-L parallel circuit is crucial for analyzing AC circuits correctly. The current through the resistor (I_R) is in phase with the supply voltage, while the current through the inductor (I_L) lags the supply voltage by 90 degrees. Therefore, the phase difference between I_R and I_L is 90 degrees, making Option 3 the correct answer. This phase relationship is a fundamental characteristic of R-L parallel circuits and is essential for accurately understanding and designing AC circuits that involve resistors and inductors.