Answer:
IV > [tex]I^{2} R[/tex]
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 = [tex]p[/tex]
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.
[tex]p[/tex] = [tex]I^{2} R[/tex] ....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 [tex]I^{2}[/tex] therefore, the electrical power delivered to the households will be less than the electrical power supplied from the power station. This means that
P > [tex]p[/tex]
equating these two powers from equations 1 and equation 3, we have
IV > [tex]I^{2} R[/tex]
