Phase relation in a parallel RL circuit: In AC analysis, does the inductor branch current lead or lag the resistor branch current in a parallel RL network? Evaluate the statement: “Inductor current leads the resistor current.”

Introduction / Context:
Phase relationships determine how currents add in AC circuits. In a parallel RL, the resistor branch current is in phase with the voltage, while the inductor branch current lags the voltage by 90 degrees (for an ideal inductor). This directly sets the phase relation between the two branch currents.

Given Data / Assumptions:

• Sinusoidal steady-state AC.
• Ideal components: resistor R and inductor L in parallel across the same voltage.
• Reference voltage is the same across both branches.

Concept / Approach:
For a resistor: i_R is in phase with v. For an inductor: v = L * di_L/dt, which leads to i_L lagging v by 90 degrees. Since v is common to both branches, i_R (in phase with v) inherently leads i_L by 90 degrees; equivalently, i_L lags i_R by 90 degrees. Therefore, the statement that the inductor current leads the resistor current is incorrect.

Step-by-Step Solution:

Verification / Alternative check:
Phasor diagram: draw I_R along the positive real axis; I_L along negative imaginary axis. The total current is the vector sum, confirming lag of the inductor branch current.

Why Other Options Are Wrong:

• Leads at low frequency / depends only on Q / only if R = X_L: None reverse the fundamental 90-degree lag for the inductor branch in the ideal case.

Common Pitfalls:
Confusing series RL behavior with parallel; mixing the inductor’s voltage-current relation with the capacitor’s, where current leads voltage.

Final Answer:
Incorrect — inductor current lags the resistor current