An engineering company is hired to improve the efficiency of a transmission line. In their report, they discuss ways that will allow them to reduce the current by a factor of four. Assuming that this is done, by what factor will the power losses be reduced?

10 months ago

Answered By Ryan H

The definition of electrical power is P = I V, where I is current and V is potential.

A transmission line should deliver an electrical potential over a distance. So here we can assume the V is a constant.

Then you might see that P is directly proportional to I, and so a fourfold reduction of current will lead to a fourfold reduction in power.

But if you like using symbols or algebra, just add subscripts for initial P and I and final P and I:

P_{0} = I_{0}V (definition of electrical power)

I_{1} = I_{0}/4 (relationship of final current to initial current)

P_{1} = I_{0}V/4 = P_{0}/4 (final power is one quarter of initial power)

10 months ago

## Answered By Ryan H

The definition of electrical power is P = I V, where I is current and V is potential.

A transmission line should deliver an electrical potential over a distance. So here we can assume the V is a constant.

Then you might see that P is directly proportional to I, and so a fourfold reduction of current will lead to a fourfold reduction in power.

But if you like using symbols or algebra, just add subscripts for initial P and I and final P and I:

P

_{0}= I_{0}V (definition of electrical power)I

_{1}= I_{0}/4 (relationship of final current to initial current)P

_{1}= I_{0}V/4 = P_{0}/4 (final power is one quarter of initial power)