Power dissipation calculation (Ohm’s law and power law): A 12 V source supplies 3 A to a resistor. Evaluate the statement: “The power dissipated by the resistor is 4 W.”

Introduction / Context:Accurate power calculations are critical for component selection and thermal design. Overheating resistors can fail catastrophically. This question checks quick application of the fundamental relation between voltage, current, and power in a purely resistive DC circuit.

Given Data / Assumptions:

• DC source voltage V = 12 V.
• Load current I = 3 A.
• Resistive load; no reactive elements are implied.

Concept / Approach:For DC resistive circuits, power dissipated by a load is P = V * I. Alternative forms using resistance are P = I^2 * R and P = V^2 / R, but those require R. With both V and I known, the direct product gives the correct result immediately.

Step-by-Step Solution:

Verification / Alternative check:Determine R from Ohm’s law: R = V / I = 12 / 3 = 4 Ω. Then compute P with P = I^2 * R = 3^2 * 4 = 9 * 4 = 36 W. Both methods agree, confirming the result.

Why Other Options Are Wrong:

• Correct / correct only if R = 1.33 Ω: Neither makes the 4 W figure right for this V and I.
• Reactive load / indeterminate with phase angle: In DC with a resistor, there is no phase; P is unambiguously V * I.

Common Pitfalls:Dropping a zero or misreading units; confusing wattage rating (how much a resistor can handle) with power actually dissipated; mixing up AC reactive cases with straightforward DC loads.

Final Answer:Incorrect