Space heater check using Ohm’s law: an electric heater draws 3.5 A from a 110 V source. Estimate the resistance of its heating element (choose the closest value).

Introduction / Context:
Household heaters are largely resistive loads. Knowing how to estimate their resistance from nameplate voltage and current is helpful for quick diagnostics and power calculations, as well as verifying that fuses and wiring are adequate.

Given Data / Assumptions:

• V = 110 V.
• I = 3.5 A.
• Ideal resistive model (ignore temperature variation for this estimate).

Concept / Approach:

Apply Ohm’s law: R = V / I. Round to the nearest answer choice. A cross-check using power P = V * I can sanity-check the result.

Step-by-Step Solution:

Verification / Alternative check:

Using P = I^2 * R → R = P / I^2 = 385 / 12.25 ≈ 31.43 Ω, same as above.

Why Other Options Are Wrong:

38.5 Ω would imply a lower current at 110 V; 385 Ω or 3.1 Ω are off by an order of magnitude and do not match the given current.

Common Pitfalls:

Arithmetic slips in division; forgetting that heater resistance changes when cold vs hot (here we use the operating point).

Final Answer:

31 Ω