In: Physics
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.
1) The resistivity of copper as a function of temperature is
where
is the resistivity of copper at (20o C)
is the reference temperature
is the temperature coefficient of copper. Hence
The plot of this function is shown below for T = 20oC to 100o C
2) The room temperature is 20oC
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.