Question

A copper wire has a radius of 1.0 mm. What is the resistance of 2m of the wire at 0 degrees C?

A. 6.3 microOhms

B. 9.9 microOhms

C. 6.3 nanoOhms

D. 9.9 milliOhms

Answer 1

The electrical resistance, R of this simple conductor is a function of its length, L and the conductors area, A. Ohms law tells us that for a given resistance R, the current flowing through the conductor is proportional to the applied voltage as I = V/R

Electrical Resistivity Equation

Where: R is the resistance in ohms (Ω), L is the length in metres (m), A is the area in square metres (m²), and where the proportional constant ρ (the Greek letter “rho”) is known as Resistivity.

The resistivity of a good conductor such as copper at room temperature 25 degree celcius is on the order of 1.72 x 10^-8 ohm metre

Area = A=πr2 = 3.14*1*10-3 2 =3.14*10-6 m2

R (at 25 deg cel )=ρla=1.72*10-8 *2 m3.14*10-6    = 10.9 mOhms

The coefficient of resistance of copper = 0.00393

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By equation

R ref= resistance at room temperature= 10.9 mOhms

The coefficient of resistance of copper = 0.00393

Resistance at 0 degree celcius= 10.9 m Ohm* (1+ 0.00393(0-20)) = 9.8917m Ohms

So the answer is option D