Electric Current: Reduce Wasted Power by 7500W

• mer584
In summary, the conversation discusses the delivery of power from a power station to a factory through wires with a total resistance of 3.0 ohms. The question is how much less power will be wasted if the electricity is delivered at a higher voltage of 50,000V instead of the current 12,000V. The conversation includes a calculation mistake and a discussion on how to properly calculate the power lost to heat in the power line. The correct answer is 7500W, and it can be found by using the formula P=I^2R with an understanding that the voltage drop across the power line is 155V.
mer584

Homework Statement

A power station delivers 620kW of power at 12,000 V to a factory through wires with total resistance 3.0 ohms. How much less power is wasted if the electricity is delivered at 50,000V rather than 12,000V?

b]2. Homework Equations [/b]
P=IV=I^2R=V^2/R V=IR

The Attempt at a Solution

So I know you need to find the current in order to be able to do this, but I'm a bit confused about when the different formulas for P can be used. The answer is 7500W.

I tried finding the current through the wire (12kV): 12kV = I(3 ohms) = 4000A
and the power lost to heat: (4000)^2 * 3 = 4.8 x 10^7 W
And the current through the wire (50kV): 50kV = I (3ohms) = 16666.67A
and the power lost to heat: (16666.67)^2 * 3 = 8.3 x 10^8 W

but these powers don't subtract to the answer. I'm not sure I understand the problem.

OK new approach since that last one seems very wrong:
I find the current at the source using P=IV
then I find how much power that dissipates by the end using P=I^2R
then I can do that same thing for when the V is higher
and subtract the two final powers...the number i got was a bit high but I think this makes more sense

Yeah, you know immediately that the first method is wrong because the power lost to heat is much much higher than the total power delivered!

The mistake was in assuming that the power line is the only "resistor" in the circuit. Something in the factory is acting as a load...i.e. it is making use of the electrical power in such a way that the total power consumption is 620 kW, which includes the factory power consumption and the power dissipated as heat in the power line. You can replace the factory with an equivalent load resistor that WOULD use up that much power when placed in series with the power line. However, since you don't know what this resistance IS beforehand, you can't solve for the current using knowledge of the voltage alone. You find I from P = VI, and then you find the portion of P dissipated in the power line from P_heat = I^2*R, GIVEN that that much current is flowing.

Or you could use P = V^2/R, provided that you understand that V here is NOT 12,000 V. V is the voltage DROP across the power line = IR = 155 V. However, it makes more sense just to use I^2 R, since you already have I. It saves you one step.

1. What is electric current and how does it relate to wasted power?

Electric current is the flow of charged particles, typically electrons, through a conductor. In the context of reducing wasted power, electric current is important because it is the main source of energy consumption in electrical devices. The higher the current, the more energy is being used, which can lead to wasted power.

2. How much power can be saved by reducing wasted power by 7500W?

By reducing wasted power by 7500W, you can potentially save up to 7500 watts of energy, which is equivalent to 7.5 kilowatts. This can result in significant cost savings on your electricity bill and also reduce your carbon footprint.

3. What are some ways to reduce wasted power in electrical devices?

Some ways to reduce wasted power include using energy-efficient appliances, unplugging devices when not in use, using power strips to easily turn off multiple devices, and using natural light instead of artificial lighting when possible. Regular maintenance and upgrades to outdated equipment can also help reduce wasted power.

4. How can reducing wasted power benefit the environment?

Reducing wasted power can greatly benefit the environment by decreasing carbon emissions and conserving natural resources. The less energy that is wasted, the less energy needs to be produced, thereby reducing the strain on natural resources and decreasing pollution from power plants.

5. Is it worth the effort to reduce wasted power?

Absolutely. Beyond the cost savings and environmental benefits, reducing wasted power can also lead to increased efficiency and longevity of your electrical devices. It also sets a good example for others and can contribute to a more sustainable future for all.

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