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A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a poten

ID: 1439373 • Letter: A

Question

A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a potential difference of 9.11 V, and the current is found to be 5.20 A. Assume a temperature of 20.0 degree C and, using this table, identify the metal out of which the wire is made. copper gold iron aluminum tungsten platinum lead silver An electronic device designed to operate at any temperature in the range from -10.0 degree C to 65.0 degree C contains pure carbon resistors. The maximum resistance of the device is what percentage higher than its minimum resistance for this range?

Explanation / Answer

Here
length ,L = 50 m

radius , r = 1 mm = 0.001 m

V = 9.11 V

current ,I = 5.2 A

let the resistivity is p

as V/I = p *L/A

9.11/5.20 = p * 50/(0.001^2 * pi)

solving for p

p = 1.101 *10^-7 Ohm.m

Now ,from the table of resistivity

the element is Platinum

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thermal coefficient of resistance of carbon ,a = -0.005 1/degree C

let the resistance at 20 degree C is R

at -10 degree C

Rmax = R * (1 + 0.005 * 30) = 1.15 *R

at T = 65 degree C

Rmin = R *(1 - 0.005 * 45) = 0.775 *R

Now , for the percentage
percentage = Rmin * 100/Rmax

percentage = 0.775 * R *100/1.15*R

percentage = 67.4 %

the answer is 67.4 %

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