Question

A copper transmission cable 140 {\rm km} long and 12.5 {\rm cm} in diameter carries a current of 115 {\rm A}.

1.What is the potential drop across the cable?
2.How much electrical energy is dissipated as thermal energy every hour?

Answer 1

Answer:

1. $V=22.0407\ V$

2. $Q=9126837\ J$

Explanation:

Given:

length of copper cable, $l=140\ km=1.4\times 10^5\ m$

diameter of copper cable, $d=12.5\ cm=0.125\ m$

current through the copper wire, $i=115\ A$

We have the resistivity of copper, $\rho=1.68\times10^{-8}\ \Omega.m$

We know that the resistance of a wire is given as:

$R=\rho.\frac{l}{a}$

where:

$a=$ cross sectional area of the wire

$R=1.68\times 10^{-8}\times\frac{140000}{\pi.\frac{0.125^2}{4} }$

$R=0.1917\ \Omega$

1.

Now from the  Ohm's law:

$V=R.i$

$V=0.1917\times 115$

$V=22.0407\ V$

2.

From the Joules law the thermal energy generated as an effect of electrical energy is mathematically given as:

$Q=i^2.R.t$

where:

$t=$ time duration for which the current flows

$Q=115^2\times 0.1917\times 3600$ (∵ we have 3600 seconds in 1 hour)

$Q=9126837\ J$