Series RL circuits — does the phase angle θ between source voltage and current increase with frequency?

Introduction / Context:
Phase angle in an RL circuit indicates how inductive the load appears. Understanding its dependence on frequency is important for filter design, power factor correction, and time response of coils and electromagnets.

Given Data / Assumptions:

• Series RL circuit driven by a sinusoidal source.
• R is frequency independent; inductor has reactance Xl = ω * L.
• Phase angle θ is defined as the angle by which current lags voltage.

Concept / Approach:
For a series RL, total impedance is Z = R + j * Xl, and the phase angle is θ = arctan(Xl / R) = arctan(ω * L / R). Since arctan is a monotonically increasing function and ω * L / R increases with frequency, θ increases with frequency from 0 degrees toward 90 degrees. Thus, the statement is correct: θ varies directly with frequency in the sense of monotonic increase.

Step-by-Step Solution:

Verification / Alternative check:
Numerical example with R = 10 Ω and L = 10 mH. At f = 50 Hz, ω ≈ 314 rad/s gives Xl ≈ 3.14 Ω and θ ≈ arctan(0.314) ≈ 17.5 degrees. At f = 5 kHz, Xl ≈ 314 Ω and θ ≈ arctan(31.4) ≈ 88.2 degrees. The increase is evident.

Why Other Options Are Wrong:

• Answering “False” would imply that θ is independent of frequency or decreases with frequency, which contradicts the arctan relation for an inductor in series with a resistor.

Common Pitfalls:
Confusing series RL with RC behavior. In an RC circuit, current leads voltage and the phase decreases toward zero as frequency rises due to capacitive reactance falling with frequency.

Final Answer:
True