A three-way 120 V lamp bulb that contains two filaments is rated for 100-200-300 W. One filament burns out. Afterward, the bulb operates at the same intensity (dissipates energy at the same rate) on its lowest as on its highest switch positions but does not operate at all on the middle position. What are the (a) larger and (b) smaller values of the filament resistances?

Question

Frederick Stein

Physics

14 June, 07:48

A three-way 120 V lamp bulb that contains two filaments is rated for 100-200-300 W. One filament burns out. Afterward, the bulb operates at the same intensity (dissipates energy at the same rate) on its lowest as on its highest switch positions but does not operate at all on the middle position. What are the (a) larger and (b) smaller values of the filament resistances?

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Answers (1)

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Lawrence Chang · Answer 1

The larger resistance value is 144 ohms and the smaller resistance value is 48 ohms.

Explanation:

Given that Resistance, R, is inversely proportional to Power, the largest value of power will yield the smallest value of resistance and vice versa.

The largest value of resistance will be:

P = V²/R

R = V²/P

R = 120²/100

R = 144 ohms

The smallest value of resistance will be:

R = 120²/300

R = 48 ohms