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:
Start with P = V * I.Solve for I: I = P / V.Substitute E = 120 V to get I numerically if P is known (e.g., 60 W → 0.5 A).
Verification / Alternative check:
If the filament resistance R were known, you could also use P = V^2 / R and then I = V / R, yielding the same I.
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:
I = P / E
Discussion & Comments