A copper transmission cable 100 km long and

Answered question

2022-05-14

A copper transmission cable 100 km long and 10.0 cm in diameter caries  a current of 125 A. What is the potential drop across the cable?

Answer & Explanation

star233

star233

Skilled2022-06-09Added 403 answers

Given 

We are given the length of the copper wire L = 100 x 103m and the is radius r=d/2=10.0 cm/2=5 cm with a current I = 125 A 

Solution 

(a) Our target is to find the potential drop across the cable. The current flows in the copper wire experiences a resistance due to the material that causes a voltage drop, so we can use Ohm's law from equations 25.9 and 25.10 to find the voltage across the wire in the next form 

V = IR = I(ρLA)

Where p is the resistivity of the copper and equals 1.72 x 10-8Ω×m and A is the cross-sectional area of the wire and equals πr2. Now we can plug our values for I, r, L and ρ into equation (1) to get the voltage

V=I(ρLπr2)=(125A)((1.72×10-8Ω×m)(100×103m)π(0.05m2))=27.4V

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