Question

In a typical transmission line, the current I is very small and the voltage V is very large. A unit length of line has resistance R. For a power line that supplies power to 10,000 households, we can conclude that:________

Answer 1

IV >
`I^(2) R`

Step-by-step explanation:

The current in the power line = I

The voltage in the power line = V

The resistance of the power line = R

Power supplied from the power house = P

power delivered to the households =
`p`

We know that the power supplied to a power line system is proportional to

P = IV ....1

we also know that according to Ohm's law, the relationship between the voltage, resistance, and current through an electrical system is given as

V = IR ....2

substituting equation 2 into equation 1, the power delivered to the households is proportional to the square of the current.

`p` =
`I^(2) R` ....3

The problem is that when power is delivered across a transmission line, some of the power is loss due to Joules heating effect of the power lines. This energy and power loss is proportional to
`I^(2)` therefore, the electrical power delivered to the households will be less than the electrical power supplied from the power station. This means that

P >
`p`

equating these two powers from equations 1 and equation 3, we have

IV >
`I^(2) R`