Electric power calculation using P = V * I in basic circuits: What is the power dissipation (in watts) of a resistor that has 24 V across it and 0.25 A flowing through it?

Introduction / Context:This question checks fundamental DC circuit analysis: calculating power dissipated by a resistor when voltage across it and current through it are known. Such computations are routine in electronics troubleshooting, sizing components, and estimating heat generation for thermal design.

Given Data / Assumptions:

• Voltage across the resistor, V = 24 V.
• Current through the resistor, I = 0.25 A.
• Assume ideal components and steady-state conditions.
• Standard power relation P = V * I applies.

Concept / Approach:Electrical power in a passive element is computed using P = V * I. Equivalent forms include P = I^2 * R and P = V^2 / R, but when both V and I are given directly, the product form is simplest and avoids intermediate steps.

Step-by-Step Solution:Start with P = V * I.Insert the values: P = 24 * 0.25.Compute: 24 * 0.25 = 6.Therefore, the power dissipated is 6 W.

Verification / Alternative check:If the resistor value were needed, R = V / I = 24 / 0.25 = 96 Ohm. Using P = I^2 * R → 0.25^2 * 96 = 0.0625 * 96 = 6 W, confirming the result.

Why Other Options Are Wrong:(a) 3 W halves the correct product; (c) 64 W mistakenly multiplies 8 * 8 or squares incorrectly; (d) 122 W has no basis in the given values; (e) is invalid because a correct answer exists.

Common Pitfalls:Mixing power formulas, arithmetic slips with decimals, or assuming RMS conversions unnecessarily in a simple DC scenario.

Final Answer:6 W.