A series RLC circuit is driven by a sinusoidal source with VT = 100 V RMS. The reactances are XL = 160 Ω and XC = 80 Ω, and the resistance is R = 60 Ω. What is the RMS current in the circuit?

Introduction:
Current in a series RLC circuit is found from the magnitude of total impedance Z. Because elements are in series, the same current flows through R, L, and C. This problem reinforces phasor addition of reactances and the Pythagorean form of impedance magnitude.

Given Data / Assumptions:

• R = 60 Ω, XL = 160 Ω, XC = 80 Ω.
• Source VT = 100 V RMS.
• Sinusoidal steady-state operation.

Concept / Approach:
For series RLC, net reactance X = XL - XC. The impedance magnitude is |Z| = sqrt(R^2 + X^2). Then I = VT / |Z|. Phase affects voltage division but not current magnitude once |Z| is known.

Step-by-Step Solution:
1) Compute net reactance: X = 160 − 80 = 80 Ω.2) Compute impedance magnitude: |Z| = sqrt(60^2 + 80^2) = sqrt(3600 + 6400) = sqrt(10000) = 100 Ω.3) Compute current: I = VT / |Z| = 100 / 100 = 1 A RMS.4) Express answer in amperes: 1 A.

Verification / Alternative check:
Check reasonableness: With |Z| = 100 Ω and 100 V RMS, current near 1 A is expected. Also, XL larger than XC indicates net inductive behavior, so current should lag voltage by arctan(X/R) = arctan(80/60), consistent with the phasor picture.

Why Other Options Are Wrong:
1 mA and 0.2 A: too small given 100 V across about 100 Ω.

6.28 A and 10 A: far too large; would require |Z| much smaller than 100 Ω.

Common Pitfalls:
Adding reactances arithmetically to resistance without squaring, or forgetting to subtract XC from XL for net X. Always use |Z| = sqrt(R^2 + (XL − XC)^2).

Final Answer:
1 A