Single-phase resistive load: A 120 V (rms) sinusoidal source feeds a 90 Ω load. What is the circuit current?

Introduction / Context:Ohm’s law in AC circuits with purely resistive loads behaves exactly as in DC: the current equals the applied rms voltage divided by the resistance. This basic calculation underpins power ratings, wire sizing, and protection-device selection in residential and industrial settings.

Given Data / Assumptions:

• RMS source voltage V = 120 V.
• Load resistance R = 90 Ω, purely resistive.
• Steady-state sinusoidal operation.

Concept / Approach:

For a resistive load, I = V / R using rms values. No phase shift exists between voltage and current, and reactive effects are absent.

Step-by-Step Solution:

Verification / Alternative check:

Power check: P = V * I = 120 * 1.333… ≈ 160 W. Alternatively, P = V^2 / R = 120^2 / 90 = 160 W. Both agree, confirming the current.

Why Other Options Are Wrong:

133 mA and 13.3 mA are off by factors of 10 and 100 relative to 1.33 A. 6.2 A would correspond to an unrealistically low resistance for 120 V (about 19 Ω), not 90 Ω.

Common Pitfalls:

Mixing peak and rms quantities; forgetting units; calculator rounding errors.

Final Answer:

1.33 A