The instructions for an electric lawn mower suggest that a 20 gauge extension co

Question

The instructions for an electric lawn mower suggest that a 20 gauge extension cord cross sectional area = 5.2 x 10" my should only be used for distances up to 35 m. For longer distances a 16 gauge extension cord should be used (cross sectional area-13x 10" m*). The resistivity of copper (used in the extension cord) is 1.72 x 10' ?.rn at 20C and the temperature coefficient of resistivity of copper is 0.004041 Cy a. What is the resistance of a 20 gauge extension cord of length 30 m at 20°c7 b. What is the resistance of a 20 gauge extension cord of length 60 m at 20°C? c. What is the resistance of a 16 gauge extension cord of length 60 m at 40°C?

Explanation / Answer

7A.

Resistance is given by:

R = rho*L/A

for 20 gauge extension cord of copper

rho = 1.72*10^-8

L = 30 m

A = 5.2*10^-7 m^2

So,

R = 1.72*10^-8*30/(5.2*10^-7)

R = 0.99 ohm

Part B

when length is 60 m

R = 1.72*10^-8*60/(5.2*10^-7)

R = 1.98 ohm

Part C

for 16 gauge extension at 20 C, resistance will be

R0 = rho*L/A

R0 = 1.72*10^-8*60/(13*10^-7) = 0.79 ohm

Now at 40 C it's resistance will be

R = R0*(1 + alpha*dT)

R = 0.79*(1 + 0.004041*(40 - 20))

R = 0.85 ohm

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