In a series RL circuit driven by a sinusoidal source, which statement correctly describes the relationship between the total source voltage and the individual voltage drops across R and L?

Introduction / Context:
Series RL circuits introduce phase differences: the resistor voltage is in phase with current, while the inductor voltage leads the current by 90 degrees. Understanding vector addition of these drops is central to AC circuit analysis.

Given Data / Assumptions:

• Sinusoidal steady state.
• Ideal R and L elements.
• Phasor relationships apply.

Concept / Approach:
The source voltage phasor V is the vector sum of VR (in phase with I) and VL (leading I by 90 degrees). Because these phasors are orthogonal components, |V| = sqrt(VR^2 + VL^2), not VR + VL. Therefore, the magnitude of the total is less than the arithmetic sum except when one term is zero.

Step-by-Step Solution:

Verification / Alternative check:
Draw a right triangle with legs VR and VL; the hypotenuse (|V|) is necessarily less than their arithmetic sum.

Why Other Options Are Wrong:

Common Pitfalls:
Adding magnitudes directly without considering phase; confusing current-phase behavior with voltage-phase behavior.

Final Answer:
The total voltage is less than the arithmetic sum of the resistor and inductor voltages.