Extension cords come in a variety of lengths and ratings. A cord with a 12-gauge

Question

Extension cords come in a variety of lengths and ratings. A cord with a 12-gauge copper wire will have a wire diameter of 2.053 mm, while a 18-gauge wire will have a diameter of 1.024 mm. The resistivity of copper is ? = 1.68 x 10-8 ?.m. Given that you want to use a 100-ft extension cord to connect an appliance to your household outlet of 120 V, answer the following:

a)         What is the voltage drop across the 12-gauge extension cord if a current of 5 A flows through it when the appliance is turned on?

b) What is the voltage drop across the extension cord if the 18-gauge cord is used instead, with the same current being drawn?

c)         How does using the 18-gauge cord in place of the 12-gauge cord affect the operation of the appliance? Be specific.

Explanation / Answer

a)

first we need to find resistance of 12 gauge

R=rho*L/A

1ft=12inches=12*2.5=30cm

A=3.14*2.0532/4

=3.3*10-6m2

=1.68*10-8*30*10-2/3.3*10-6

=0.0015ohms

V=0.0015*5

=0.075V

b)

A=3.14*1.0242/4

=0.823*10-6m2

=1.68*10-8*30*10-2/0.823*10-6

=0.0061ohms

V=0.0061*5

=0.031V

c)

18 guage is having high resistance

12 guage is having less resistance

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