A three-way lightbulb has two filaments with resistances R 1 and R 2 connected i

Question

A three-way lightbulb has two filaments with resistances R1 and R2 connected in series. The resistors are connected to three terminals, as indicated in the figure (Figure 1) , and the light switch determines which two of the three terminals are connected to a potential difference of 120 V at any given time. When terminals A and B are connected to 120 V the bulb uses 85 W of power. When terminals A and C are connected to 120 V the bulb uses 50 W of power.

A) What is the resistance R1?

B) What is the resistance R2?

C) How much power does the bulb use when 120 V is connected to terminals B and C?

Explanation / Answer

Using Power = Voltage^2 / Resistance

a) R1 = 120^2 / 85 = 169.411 ohms ------------------------------------------answer )

b) (R1 + R2) = 120^2 / 50 = 288 ohms, so R2 = 118.589 ohms ===================answer)

c) P = 120^2 / 118.589 = 121.42watts ========================answer)

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