A 1.70m cylindrical rod of diameter 0.550cm is connected to a power supply that

Question

A 1.70m cylindrical rod of diameter 0.550cm is connected to a power supply that maintains a constant potential difference of 12.0V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0 ?C) the ammeter reads 18.8A , while at 92.0?C it reads 17.3A . You can ignore any thermal expansion of the rod.

Part A

Find the resistivity and for the material of the rod at 20 ?C.

Part B

Find the temperature coefficient of resistivity at 20 ?C for the material of the rod.

Explanation / Answer

use ohms law as V = iR in each case

at temp t = 20 degC , R20 = V/i = 12/18.8 = 0.638 ohms

at t   = 92 degC , R92    =   12/17.3 = 0.694 ohms

now use

Rt = Ro ( 1+ A DT)

where here DT    92-20 = 72 deg

A is Alpha = temp Coefiiciient of Ressiatnce

so

1+A DT = 0.694/0.638

1+ADT = 1.0877

A DT = 1.0877-1 = 0.0877

A = 0.0877/72

A = 1.21 *10^-3 ohm m -<<<<<<<<<<<Answer to aprt B

---------------------------------------

resistivity Rho = RA/L

rho = (0.638 * 2*3.14 * 0.0055* 1.7/(2*1.7)

rho = 1.1*10^-2 Ohm m---------------<<<<<<Answer topart A

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