A three-way lightbulb has two filaments with resistances R1 and R2 connected in

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.

What is the resistance R1?

What is the resistance R2?

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

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

c) P = 120^2 / 118.589 = 121.427 watts

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