Question

In: Physics

A thin spherical shell of radius R and total charge Q distributed uniformly over its surfacce....

A thin spherical shell of radius R and total charge Q distributed uniformly over its surfacce.

1. Plot resistitivity as a function of temperature for some resonable range of temeratures.

2. Design a resistor made of copper that has a resistance of 50 Ohms at room remperature.

Solutions

Expert Solution

1) The resistivity of copper as a function of temperature is

where

is the resistivity of copper at (20^o C)

is the reference temperature

is the temperature coefficient of copper. Hence

The plot of this function is shown below for T = 20^oC to 100^o C

2) The room temperature is 20^oC

At this temperature, the resistivity of copper is

Suppose we want the resistor's length to be L = 1 cm or 0.01 m

Then for a 50 ohm resistor

The cross sectional area needed for the resistor is

The resistor is in the form of a cylinder which has a circular cross section. Hence the area of the circle is

The radius of the circle is

The diameter of the copper wire needs to be

Hence for a 50 ohms copper resistor at room temperature, you need a copper wire of length 1 cm and diameter 2.07 micrometers.

genius_generous answered 1 year ago

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