Household lamp resistance from nameplate values: Which formula directly gives resistance R when the rated power P and voltage E of a light bulb are known?

Introduction / Context:
Nameplates list voltage and power ratings. From these, one can estimate the operating resistance of a lamp. This is useful for quick checks and for calculating expected current draw on a circuit.

Given Data / Assumptions:

• E denotes voltage; P denotes power; R denotes resistance; I denotes current.
• Assume steady-state operation at the rated conditions.
• Ignore temperature dependence for this idealized calculation.

Concept / Approach:
Starting from P = E * I and Ohm’s law E = I * R, eliminate I. Substituting I = E / R into P = E * I gives P = E^2 / R. Rearranging yields R = E^2 / P.

Step-by-Step Solution:
Ohm’s law: E = I * R.Power law: P = E * I.Eliminate I: I = E / R → P = E * (E / R) = E^2 / R.Solve for R: R = E^2 / P.

Verification / Alternative check:
Dimensional analysis: volts^2 / watts yields ohms, consistent with resistance.

Why Other Options Are Wrong:
(b) P = P * R is nonsensical; (c) is the unsolved form before isolating R; (d) gives current, not resistance; thus only (a) directly produces R from E and P.

Common Pitfalls:
Stopping at P = E^2 / R and forgetting to rearrange; misreading E2 as E * 2 instead of E squared.

Final Answer:
R = E2/P.