Question

A copper transmission cable 100 km long and 10.0 cm in diameter carries a current of 125 A. (a) What is the potential drop across the cable? (b) How much electrical energy is dissipated as thermal energy every hour?

Answer 1

Answer: (a) The potential drop across the cable is 27.4V

(b) The electrical energy loss every hour is 12.3MJ

Explanation: See attachment below

Answer 2

(a) The potential drop across the cable is 27.5 V

(b) 12.375 J of electrical energy is dissipated as thermal energy.

Electrical energy and potential difference:

(a) According to Ohm's Law, the potential drop is given by:

V = IR

where I is the current, and

R is the resistance of the wire.

The resistance R is given by:

$R=\frac{\rho L}{A}$

where ρ is the resistivity of copper = $1.7\times18^{-8} \Omega /m$

L is the length = 100km = 10000m

and A is the cross-sectional area given by:

$A = \frac{\pi d^2}{4} =\frac{3.14\times(10\times10^{-2})^2}{4} =7.85\times10^{-3}\;m^2$

So, the resistance is:

$R=\frac{1.7\times10^{-8}\times10000}{7.85\times10^{-3}}\\\\R= 0.22 \Omega$

hence, the voltage drop:

V = 125 × 0.22 V

V = 27.5V

(b) Te electrical energy dissipated is given by:

E = Pt

where P= VI  is the electrical power, and

t is the total time

$E =VIt\\\\E=27.5\times125\times3600\\\\E=12.375 \;MJ$

Learn more about resistivity:

https://brainly.com/question/16274053?referrer=searchResults