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

Question

A three-way light bulb has two filaments with resistances R1 and R2 connected in series. The resistors are connected to three terminals, as indicated in the figure , 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 63.0 W of power. When terminals A and C are connected to 120 V the bulb uses 47.0 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? W

Explanation / Answer

When terminals A and B are connected to 120 V the bulb uses 63.0 W of power

P = V2/R1 = 63

R1 = 228.57 ohm (ans)

When terminals A and C are connected to 120 V the bulb uses 47.0 W of power.

P = V2/(R1+R2) =47

(R1+R2) =1202/47=306.38 ohm

So R2 = 306.38 - R1 = 77.81 ohm (ans)

Power across R2 = 1202/77.81 = 185.06 W (ans)

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