Find resistance of aluminium wire of length 25 cm and cross section radius 1 mm.

Question

Find resistance of aluminium wire of length 25 cm and cross section radius 1 mm. Assume a perfectly stretchable resistor with resistance R, length L and cross section area A. Let's stretch our resistor to length 4L, what is its resistance now? Consider resistor from part a (aluminium wire). If initially it was at temperature 20 C (and resistance that you found in a), what is the resistance of the wire at 80C? For aluminium resistivity p = 2.65 * 10^_B ohm m and temperature coefficient alpha = 0.00429 K^-1.

Explanation / Answer

a) Resistivity of Aluminum = = 2.65*10^-8 ohm m

Then R = *L/A = (2.65*10^-8*0.25)/(pi*10^-6) = 0.0021088 ohm = 2.1 m-ohm

b) As R = *L/A   where and A are contants.

So, With stretching the length to 4L, Resistance will be four times i.e. 8.4 m-ohm

c) As R = Ro[1 + a*(T2 - T1)] = 2.1*10^-3[1 + 0.00429*60] = 2.64 m-ohm

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