Suppose you need to install two heaters, which will be powered by conventional r

Question

Suppose you need to install two heaters, which will be powered by conventional residential power, i.e. V=120. V, and are to be controlled by a single on-off switch. Each heater works by dissipating power in a resistor. The first heater, with resistance R1, is to produce P1=410. W. The second, with resistance R2, is to produce P2=1080 W.

a) If the two heaters are to be wired in series, what should R1 and R2 be? (Enter your answer for R1 first.)

b) If the two heaters are to be wired in parallel, what should R1 and R2 be?

Explanation / Answer

a) If they are in series, voltage gets divided. So, 410=V1^2/R1, 1080=(120-V1^2)/R2

Current is same throughout, so V1/R1=V2/R2= (120-V1)/R2. Solving for V1,

V1=120*R1/(R1+R2).

Then solving for R1 and R2, we get

R1= 41 ohms, R2= 108 ohms.

b) If they are in parallel, voltage remains same. So, 410=120^2/R1, 1080=(120^2)/R2

So, R1= 35.12 ohms, R2= 13.33 ohms.

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