One question, should be a quickie

[ninoslino]

1. You connect two coils of the same resistance in series to a constant-voltage line. When you later connect them in parallel to the same line, the heat developed per minute, compared with the former rate is
a) the same
b) twice as great
c) one half as much
d) four times as great
e) one fourth as much

Now this is what I was thinking... since the ratio of the Reff series to Reff parallel would be 4:1, which means that the resistance would be 4 times greater in the series circuit and the resistance is proportional to the amount of heat lost... therefore the heat developed per minute would be 4 times greater. And since we want the parallel comapred to former, so parallel(heat)/former(heat) = 1/4 = one fourth = e.

Is there a flaw in my way of thinking? Thank you for your time guys (or girls).

 

[Doc Al]

Welcome to PF!

Now this is what I was thinking... since the ratio of the Reff series to Reff parallel would be 4:1, which means that the resistance would be 4 times greater in the series circuit

Right. So far, so good.

and the resistance is proportional to the amount of heat lost...

No. The rate of heat generated is the power consumed by the resistor. $P = VI = V^2/R$, so the power is proportional to the inverse of the resistance.

 

[ninoslino]

Thank you doc!