In a series RLC circuit driven by an AC source of RMS voltage V, the current magnitude can be determined using which relationship?

Introduction:
Finding current in a series RLC circuit is a fundamental task in AC analysis. Because resistance and reactance combine vectorially, the current cannot be obtained from the resistance alone unless the reactance is zero. This question ensures familiarity with impedance-based current calculation.

Given Data / Assumptions:

• Series RLC circuit, sinusoidal steady state.
• Source RMS voltage is V.
• Impedance magnitude is Z = sqrt(R^2 + (XL − XC)^2).

Concept / Approach:
Ohm’s law in AC form uses complex impedance: I = V / Z (phasor form). For magnitudes, I = |V| / |Z|. In a series RLC, Z depends on both resistance and the net reactance (XL − XC). Therefore, current is determined by the total impedance, not just R or a simple sum of reactances.

Step-by-Step Solution:
1) Compute reactances: XL = 2 * pi * f * L, XC = 1 / (2 * pi * f * C).2) Find net reactance: X = XL − XC.3) Calculate impedance magnitude: Z = sqrt(R^2 + X^2).4) Apply AC Ohm’s law for magnitude: I = V / Z.

Verification / Alternative check:
At resonance (XL = XC), Z reduces to R, and the formula becomes I = V / R, which is a special case consistent with I = V / Z.

Why Other Options Are Wrong:
I = V / R: true only when XL = XC (resonance) or when reactance is negligible; not generally correct.I = V / (XL + XC): ignores the vector difference and the resistance component; not an impedance magnitude.I = V * Z: dimensionally incorrect; would increase current with impedance, which contradicts physics.

Common Pitfalls:
Adding reactances algebraically without considering phase, or forgetting to include resistance in the impedance calculation.

Final Answer:
I = V / Z