The electrical resistance R of a wire varies directly as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain alloy has a
resistance of 36 ohms. What is the resistance of a piece of wire 60 meters long and 1.2 centimeters in diameter made from the same material?
2006-10-26 03:57:46 · 7 answers · asked by Dennis B 1 in Science & Mathematics ➔ Mathematics
since the length is 3times so the resistance goes upto 36*3= 108ohms.
the diameter changes by 2times. so the div is by 4.
108/4= 27ohms----answer
2006-10-26 04:12:06 · answer #1 · answered by Charu Chandra Goel 5 · 0⤊ 0⤋
Directly with length, this means that a 60 m cable will have 3 times the resistance of a 20 m one of the same diameter.
Inversely with the square of the diameter means that a cable 0.6 diameter will have 4 times more resistance than one double the diameter (2^2=4).
So you go from 20 to 60: resistance is 3 times higher.
You go from 0.6 to 1.2 cm: resistance is 4 times lower.
You have 36 ohm for 20 m at 0.6 cm, so you will have 36*3/4 = 27 ohm for a cable 60 m that is 1.2 cm in diameter.
2006-10-26 11:03:38 · answer #2 · answered by Vincent G 7 · 1⤊ 0⤋
Multiplying the length by 3 multiplies the resistance by 3, due to direct proportionality. Multiplying the diameter by 2 divides the resistance by 2^2 = 4 due to inverse square proportionality. The net factor is 3/4 = 0.75. Multiply the original resistance of 36 ohms by the factor.
2006-10-26 11:01:23 · answer #3 · answered by DavidK93 7 · 0⤊ 0⤋
DavidK93 and Vincent G are on the right track. Errors exist in DanE's response (used 20 ohms instead of 36 ohms for the resistance) and kagerendan's response (didn't square the diameter).
2006-10-26 11:14:53 · answer #4 · answered by billclawson 2 · 0⤊ 0⤋
Compare the ratios:
20 m / .6^2 and 60 m / 1.2^2
20/.36 and 60/1.44
55.555 and 41.667
divide 41.667 by 55.555 = .75; therefore, R2 = .75 R1 and the second wire would have less resistance than the first.
2006-10-26 11:21:04 · answer #5 · answered by Doug R 5 · 0⤊ 0⤋
three times the length would give it 3 times the resistance
twice the diameter would give it 1/4 the resistance
putting them together would give
(20 * 3) / 4 = 15
2006-10-26 11:01:10 · answer #6 · answered by DanE 7 · 0⤊ 0⤋
Should be 54 ohms.
2006-10-26 11:01:31 · answer #7 · answered by Anonymous · 0⤊ 0⤋