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?

Question

Solve this multiple-choice question and choose the correct option.

Curioustab · Accepted Answer

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:1) Set VR = I * R, in phase with I.2) Set VL = I * X_L, leading I by 90 degrees.3) Compute |V| using |V| = sqrt(VR^2 + VL^2).4) Conclude |V| 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:Equal to arithmetic sum: Ignores phase; voltages are not colinear.Same amplitude and phase everywhere: False in RL; phase differs across L.Exactly 90 degrees lag: True only for pure inductors; RL phase is between 0 and 90 degrees.None of the above: Option C is correct.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.

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?

Answer

Explanation