Solve Electrical Power Homework: 5.3kW

[Jstew]

Homework Statement

A power station delivers 520 kW of power to a factory through wires of total resistance of 3ohms. How much less power is wasted if the electricity is delivered at 50000V instead of 12000V?

Homework Equations

$$V=IR$$
$$P=IV=I^{2}R=\frac{V^{2}}{R}$$

The Attempt at a Solution

$$\frac{(50000V)^{2}}{3ohms}=8.3x10^{8}W$$

$$\frac{(12000V)^{2}}{3ohms}=4.8x10^{7}W$$

$$8.3x10^{8}W-4.8x10^{7}W=7.82x10^{8}W$$

The correct solution, verified by a classmate and the answer key, is 5.3kW
What have I done incorrectly?

 

[ChillyWilly]

Yes the asnwer is 5.3kW

What you have done is partly correct, but it is the last step. You have not used your other given equation. Try and use this first equation and solve for the unknown then calculate the power wasted by each.

Remember you are looking for power "wasted" so think voltage "wasted" or in more electrical terms voltage drop in the lines from the plant to the factory.

I hope this helps you out.

 

[Jstew]

Ok, I found the current first and then, using the power equation with current and resistance, found the power wasted. This gives the correct answer of 5.3kW. However, conceptually, I'm still unclear as to why the two methods give different answers.

 

[edziura]

The method you used assumes that, for example, all 12,000 V are dropped across the power line and none across the factory (load). In fact, most of the voltage is dropped across the factory and only a small fraction across the power line. Now that you know the current, you can verify this.