The most common material used for sandpaper, silicon carbide, is also widely use

Question

The most common material used for sandpaper, silicon carbide, is also widely used in electrical applications. One common device is a tubular resistor made of a special grade of silicon carbide called carborundum. A particular carborundum resistor (see the figure) consists of a thick-walled cylindrical shell (a pipe) of inner radius a = 1.89 cm, outer radius b = 2.89 cm, and length L = 59.7 cm. The resistance of this carborundum resistor at 20 degreeC Is 1.057 Ohm. Calculate the resistivity of carborundum at room temperature. Carborundum has a high temperature coefficient of resistivity: o = 2.14·10-3 K-1. If, in a particular application, the carborundum resistor heats up to 349.0 degreeC, what is the percentage change in its resistance between room temperature (20.0 degreeC) and this operating temperature?

Explanation / Answer

a)cross sectional area A = (b2 - a2 ) = (2.892-1.892) =15.02 cm2

length L = 59.7 cm

resistance R =1.057

if the resistivity is then = R*A/L = 1.057*15.02/59.7 =0.266 -cm = 0.00266 -m

b) change in resistivity = x T = 2.14 x 10-3 * (349-20) =0.704 -cm

new resistivity '= 0.266 + 0.704 =0.970 -cm

new resistance R' = ' L/A =3.855

hence % change in resistance = (R' - R)*100 /R =264.7 %

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