Power dissipation vs. resistor ratings: A 33 Ω 0.5 W resistor and a 330 Ω 0.5 W resistor are each connected across a 12 V source (parallel branches). Which resistor(s) will overheat based on power dissipation?

Introduction / Context:
Selecting safe resistor power ratings prevents failures and fire hazards. This problem reinforces the calculation of power from a fixed voltage across resistors and comparison with nameplate ratings.

Given Data / Assumptions:

• Two separate resistors are each placed directly across 12 V.
• Ratings: 0.5 W (half-watt) each.
• Resistances: 33 Ω and 330 Ω.

Concept / Approach:
With a known voltage across a resistor, use P = V^2 / R to compute dissipation. If the computed power exceeds the rated wattage, the part is likely to overheat in continuous service.

Step-by-Step Solution:

Verification / Alternative check:
Check current for 33 Ω: I = V / R = 12 / 33 ≈ 0.364 A; P = V * I ≈ 12 * 0.364 ≈ 4.37 W. Consistent with the V^2 / R result.

Why Other Options Are Wrong:

• 330 Ω: Calculated power is below 0.5 W.
• Both resistors / neither resistor: Contradicted by the computed values.

Common Pitfalls:

• Forgetting that resistors in separate branches each experience the source voltage.
• Using P = I^2 * R without first finding I correctly.

Final Answer:
33 Ω