Phase angle trend: As the frequency of the applied AC voltage increases in a series RL circuit, how does the current–voltage phase angle (|θ|) change?

Introduction / Context:The phase angle between source voltage and current in a series RL depends on the ratio XL/R. Understanding how this ratio shifts with frequency is crucial for filter design and transient response intuition.

Given Data / Assumptions:

• Series RL with fixed R and L.
• Frequency f increases.
• θ = arctan(XL / R) (current lags voltage by θ in inductive circuits).

Concept / Approach:Since XL = 2 * pi * f * L, increasing f increases XL while R is constant. Therefore, XL / R increases, and θ = arctan(XL / R) increases monotonically toward 90° as frequency becomes very large.

Step-by-Step Solution:

Verification / Alternative check:Bode intuition: The RL corner frequency fc = R / (2 * pi * L) marks where θ ≈ 45°. Above fc, the circuit becomes increasingly inductive, confirming the trend of increasing |θ|.

Why Other Options Are Wrong:

• 'decreases' or 'does not change': Contradict the XL dependence on frequency.
• 'cannot be determined': The direction is determinable independent of specific values.
• 'becomes zero immediately': Zero angle happens only at DC (f → 0) for ideal RL.

Common Pitfalls:

• Confusing series and parallel behavior; in parallel RL, current components behave differently but θ of branch currents is defined separately.

Final Answer:increases