SOLUTION: a wire of length 20 m and diameter 0.6 cmTHE 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 A
Question 62972: a wire of length 20 m and diameter 0.6 cmTHE 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? Answer by uma(370) (Show Source):
You can put this solution on YOUR website! Let K be the constant of proportionality.
Then r = K*l/(d^2) wher d is the diameter.
Given that a wire of length 20 m and diameter 0.6 cm has a resistance of 36 ohms
==> 36 = K* 2000/((0.6)^2)
==> 36 = K*2000/(0.36)
Multiplying both the sides by 0.36/2000 we get,
36*(0.36/2000) = K
==> 0.00648 = K
Now the equation for resistance becomes,
r = 0.00648*l/(d^2)
When l = 6000cm and d = 1.2 cm
r = 0.00648 *(6000/(1.2)^2
==> r = 0.00648 * (6000/1.44)
==> r = 27
Thus the resistance of 20 m long wire with diameter 1.2cm is 27 ohms.
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