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

1.
`V=22.0407\ V`

2.
`Q=9126837\ J`

Step-by-step explanation:

Given:

length of copper cable,
`l=140\ km=1.4* 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*10^(-8)\ \Omega.m`

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

`R=\rho.(l)/(a)`

where:

`a=` cross sectional area of the wire

`R=1.68* 10^(-8)*(140000)/(\pi.(0.125^2)/(4) )`

`R=0.1917\ \Omega`

1.

Now from the Ohm's law:

`V=R.i`

`V=0.1917* 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* 0.1917* 3600` (∵ we have 3600 seconds in 1 hour)

`Q=9126837\ J`