Effect of source amplitude in a linear RL series circuit (frequency fixed): If the source voltage magnitude V_S increases while component values and frequency remain unchanged, which statement about the circuit's behavior is correct?

Introduction / Context:In linear AC circuits (such as a series RL network), the relationship between source voltage, current, and impedance at a fixed frequency follows a direct proportionality: I = V_S / |Z|. This question tests recognition of which quantities change when the source voltage is varied while the circuit's impedance stays constant because R, L, and f are unchanged.

Given Data / Assumptions:

• Series RL circuit with fixed R and L.
• Operating frequency is fixed, so X_L = 2 * pi * f * L is constant.
• Linear components; no saturation or nonlinearity.
• We consider steady-state sinusoidal operation.

Concept / Approach:The circuit impedance magnitude |Z| = sqrt(R^2 + X_L^2) is constant when R, L, and f do not change. Therefore, increasing the source voltage magnitude V_S increases current magnitude proportionally, I = V_S / |Z|. The phase angle theta = arctan(X_L / R) is also constant because it depends only on R and X_L at the given frequency. Real power P = I^2 * R increases with I, not decreases.

Step-by-Step Solution:

Verification / Alternative check:Doubling V_S while holding |Z| constant doubles I. With P proportional to I^2 for a fixed R, power quadruples, consistent with basic AC power relations.

Why Other Options Are Wrong:

• Impedance increases: |Z| depends on R and X_L, not V_S.
• Real power decreases: incorrect; as I rises, P = I^2 * R rises.
• Phase angle increases: theta depends on R and X_L only.
• Reactive power magnitude decreases: Q = I^2 * X_L rises with I.

Common Pitfalls:Assuming source voltage influences impedance; confusing voltage-scaling effects with frequency changes; forgetting that both real and reactive power scale with I^2 for fixed R, X_L.

Final Answer:Current increases