Household bulbs rated at power P and operating at 120 V: which equation most directly gives the current rating I?

Introduction / Context:Labeling on household bulbs typically specifies power (watts) at a nominal line voltage (e.g., 120 V). To determine current draw, the simplest relation uses the definition of electric power for a load: P = V * I. This gives a direct way to compute the current rating from nameplate values.

Given Data / Assumptions:

• Nominal operating voltage E = 120 V (rms).
• Power rating P given in watts.
• We seek the current I under nominal conditions.

Concept / Approach:

• Use P = V * I for steady-state AC with resistive loads (or apparent power S = V * I for general loads; bulbs are predominantly resistive when hot).
• Rearrange to I = P / E.
• Other power identities (I^2 R and V^2 / R) are equivalent but require R, which is not given.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• P = I^2 R and P = E^2 / R: Correct identities but not the most direct here because R is unknown.
• P = I E: True but not explicitly solved for I; the option 'I = P / E' directly gives the current.
• None of the above: Incorrect because 'I = P / E' is correct and most direct.

Common Pitfalls:

• Confusing peak and rms values; nameplate values use rms.
• Ignoring that filament resistance changes with temperature; nameplate current corresponds to hot operating condition.

Final Answer: