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 = 1.5 cm, outer radius b = 2.5 cm, and length L = 60 cm. The resistance of this carborundum resistor at 20 °C is 0.797 O.

a) Calculate the resistivity of carborundum at room temperature.

b) Carborundum has a high temperature coefficient of resistivity: a = 2.14·10^-3 K^–1. If, in a particular application, the carborundum resistor heats up to 300.0 °C, what is the percentage change in its resistance between room temperature (20.0 °C) and this operating temperature?

Explanation / Answer

Resistance = l/A

Resistivity = R * A/l = 0.797 * (2.5^2 - 1.5^2)*10^-4 / 0.6 = 16.68 *10^-4 m

R 300 = R 20 (1+ k (300-20))

Percentage change = ((R 300 - R 20) / R 20) *100 = 280k *100 = 59.92%

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