For a 100 Hz series RLC circuit with source voltage VS = 20 V, total resistance RT = 66 ohms, and total reactance XT = 47 ohms, what is the circuit current magnitude I?

Introduction:
This question tests the ability to compute current in a series RLC circuit when total resistance and total reactance are known. The key step is forming the magnitude of the total impedance and then applying Ohm's law with RMS quantities.

Given Data / Assumptions:

• VS = 20 V (RMS).
• RT = 66 ohms.
• XT = 47 ohms (net reactance, sign not needed for magnitude).
• Frequency is 100 Hz; frequency value is not needed once RT and XT are given.

Concept / Approach:
For a series circuit, total impedance is Z = RT + j * XT with magnitude |Z| = sqrt(RT^2 + XT^2). The RMS current is I = VS / |Z|. If the sign of XT were required for phase, it would affect the angle but not the magnitude of current.

Step-by-Step Solution:

Verification / Alternative check:
A quick sanity check: with RT alone, current would be 20 / 66 ≈ 0.303 A. Adding reactance increases |Z| to about 81 ohms, reducing current to about 0.25 A, which is consistent with the detailed calculation.

Why Other Options Are Wrong:

• 1.05 A: Far too high; would require |Z| ≈ 19 ohms, not supported by data.
• 303 mA: This is 20 / 66 and ignores the reactance contribution.
• 107 mA: Too low; would imply |Z| ≈ 187 ohms, inconsistent with RT and XT provided.

Common Pitfalls:
Adding RT and XT arithmetically instead of vectorially, forgetting to take the square root in |Z|, or mixing up RMS and peak values. Also, do not confuse the sign of XT; it affects phase, not current magnitude.

Final Answer:
247 mA.