Series RL current control: To increase the current in a series RL circuit, should the excitation frequency be increased, decreased, or kept constant?

Introduction / Context:
In series RL circuits, current depends on the magnitude of the impedance, which is a function of resistance and inductive reactance. Frequency manipulation is a common way to control current in AC networks and power electronics.

Given Data / Assumptions:

• Series RL circuit with resistance R and inductance L.
• Inductive reactance XL = 2 * pi * f * L.
• AC source voltage magnitude is fixed.

Concept / Approach:
Total impedance magnitude in series RL is Z = sqrt(R^2 + XL^2). Since XL grows with frequency, increasing frequency increases Z, which decreases current I = V / Z. Therefore, to increase current, frequency must be reduced so that XL decreases.

Step-by-Step Solution:
XL = 2 * pi * f * LZ = sqrt( R^2 + XL^2 )I = V / ZDecrease f ⇒ decrease XL ⇒ decrease Z ⇒ increase I

Verification / Alternative check:
Example: R = 10 Ω, L = 50 mH. At 100 Hz, XL ≈ 31.4 Ω; at 50 Hz, XL ≈ 15.7 Ω. Z reduces from ≈ 33.9 Ω to ≈ 18.5 Ω, so current nearly doubles for the same applied voltage, validating the conclusion.

Why Other Options Are Wrong:

• Should be increased: Would increase XL and reduce current.
• Should be constant / cannot be determined: The direction of change is determined from formulas and does not require numeric values.

Common Pitfalls:
Confusing series and parallel behavior, or forgetting that inductive reactance is proportional to frequency in all linear inductors.

Final Answer:
should be decreased