An engineer needs a resistor with zero overall temperature coefficient of resist

Question

An engineer needs a resistor with zero overall temperature coefficient of resistance at . She designs a pair of circular cylinders, one of carbon and one of Nichrome as shown below. The device must have an overall resistance of R1 + R2 = 10.0 ? independent of temperature and a uniform radius of r = 1.50 mm. Can she meet the design goal with this method? If so, state what you can determine about the length l1 and l2 of each segment. You may ignore thermal expansion of the cylinders and assume both are always at the same temperature.

Explanation / Answer

we know,
R = pl/A
here, A1 = A2 = pi* (1.50 mm) ^ 2

and R1 + R2 = 10
R1 = p1 * l1 / A1
R2 = p2 * l2/ A2

if you know the resistivity of the materials, p1 and p2, then you can calculate the ratio of l1 and l2 from these equations. To get their exact value, you will need more data.

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