For the three-way bulb (50 W, 100 W, 150 W) discussed in Conceptual Example 11, find the resistance of (a) the 100-W filament and (b) the 50-W filament. Assume that the wattage ratings are not limited by significant figures and ignore any heating effects on the resistances. (a) Number Units (b) Number i Units VEXAMPLE 11 | The Physics of a Three-Way Light Bulb Threeway light bulbs are popular because they can provide three levels of illumination (e.g., 50 W, 100 W, and 150 W) using a 120-V socket. The socket, however, must be equipped with a special threeway switch that enables one to select the illumination level. This switch does not select different voltages, because a threeway bulb uses a single voltage of 120 V. Within the bulb are two separate laments. When the bulb is producing its highest illumination level and one of the laments burns out (i.e., vaporizes), the bulb shines at one of the other illumination levels (either the lowest or the intermediate one). When the bulb is set to its highest level of illumination, how are the two laments connected, (at) in parallel or (b) in series? Reasoning In a series connection, the laments would be connected in such a way that there is the same current through each one. The current would enter one lament and then leave that lament and enter into the other one. In a parallel connection, the same voltage would be applied across each lament, but the current through each would, in general, be different, the two currents existing independently of one another. Answer (b) is incorrect. If the laments were wired in series and one of them burned out, no current would pass through the bulb and none of the illumination levels would be available, contrary to what is observed. Therefore, the laments are not wired in series. Answer (a) is correct. Since the laments are not in series, they must be in parallel, as Interactive Figure 20.22 helps to explain. The power dissipated in a resistance R is P: V2,,\" / R, according to Muation M59 With a single value of 120 V for the voltage Vrms, three different power ratings for the bulb can be obtained only if three different values for the resistance R are available. In a 50-W/100-W/150-W bulb, for example, one resistance R50 is provided by the 50-W lament, and the second resistance R100 comes from the looW lament. The third resistance R150 is the parallel combination of the other two and can be obtained from 1/R150 = 1/R50 + 1/Rioo- Interactive Figure 20.22 illustrates a simplied version of how the threeway switch operates in such a bulb. The rst position of the switch closes contactA and leaves contact B open, energizing only the 50-W lament. The second position closes contact B and leaves contactA open, energizing only the looW lament. The third position closes both contacts A and B, so that both laments light up to give the highest level of illumination. Related Homework: Problem 51 507W lilament lOOrW filament B "Simplified verSIon of 3-way switch In lamp socket