Answer :
To find the appropriate power rating for a 220 V system, the original 25 W power rating at 110 V is scaled up considering the resistance of the bulb remains constant. The new power rating for the bulb at 220 V is calculated to be 100 W. Thus, the correct rating for the electric bulb for a 220 V system would be option 2) 100 W, 220 V.
The question concerns an electric bulb that consumed 25 W of power when operated at 110 V and inquiring about the correct rating of the bulb should it be designed for 220 V instead.
The relationship between power (P), voltage (V), current (I), and resistance (R) is described by the formulas:
P = VI and V = IR.
Thus, by rearranging the formula, we can write[tex]P = I^2R.[/tex]
If the voltage is doubled and the resistance remains constant, the power will increase by a factor of four (since P is proportional to the square of the voltage when resistance is constant).
For an electric bulb rated at 25 W for 110 V, if the voltage increases to 220 V and the bulb's resistance doesn't change, the new power rating P' would be:
[tex]P' = (V'^2 / V^2) \times P = (220^2 / 110^2) \times 25 W = 4 \times 25 W = 100 W[/tex]
Therefore, the correct rating for the bulb for operation at 220 V is option 2) 100 W,220 V.
