physics helppp?

Question

man wishes to vacuum his car with a canister vacuum cleaner marked 550 W at 120 V. The car is parked far from the building so he uses an extension cord 15.0 m long to plug the cleaner into a 120 V source. Assume that the cleaner has constant resistance.
(a) If the resistance of each of the two conductors of the extension cord is 0.900 , what is the actual power delivered to the cleaner?
W
(b) If, instead, the power is to be at least 540 W, what must be the diameter of each of the two identical copper conductors in the cord the young man buys?
mm
(c) Repeat part (b) if the power is to be at least 547 W. [Suggestion: A symbolic solution can simplify the calculations.]
mm

Answer 1

First, consider the power equation
P=V*I

Then, using ohm's law,
V=I*R
or I=V/R
so
P=V^2/R

The nominal rating is:

550=120^2/R
R=120^2/550
=26.18 ohms

By introducing the long extension cord, the actual resistance is now:

26.18+1.800
=27.98

The new power is
120^2/27.98
514.7 W

If you want 540W
R=120^2/540
R=26.67 Ohms
Subtract 26.18 to find the resistance of 30 meters of wire

Same with C

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