Power companies send electricity at extremely high voltages because lower current means less energy lost. But here's the thing I don't get about that. Let's say (100% hypothetical numbers here, don't fixate on that) you've got a 100 volt circuit at ten amps and ten ohms (V = I * R, 100 = 10 * 10). Now you step that up so it's 1000 volts, which decreases the amps to one (because 100 * 10 = 1000 * 1, same total energy output) and increases the ohms to 1000. Why doesn't the tenfold increase in resistance cause as much more energy loss than the reduction of current? What's the math behind this?
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The savings come from losses in the connecting wires, not the load.
Say you have a 100 watt lamp, and you want to light it at the end of a long transmission line 100 kilometers long. Say the line has a resistance of 100 ohms.
Now you could design the lamp so that it runs from 100 volts. So to use 100 watts of electricity, it must have a resistance of 100 ohm (100 volts / 100 ohm = 1 amp, and then 100 volts x 1 amp = 100 watts).
but, becuase of the long transmision line, the generator at the end 'sees' not 1 ohm, but 200 ohms! To get 1 amp through the line to light the lamp, the generator must produce 1 amp x 200 ohms = 200 volts. The extra 100 volts is 'lost' in the resistance of the transmission line. Nopw since the transmission line is (in this example) just like a resistor, it will dissipate power just like the lamp (it will get warm). The power lost as heat will be 100 volts (voltage dropped across the resistance of the line) x 1 amp (current through the line) = 100 watts ! So we are only 50% efficient here, to get 100 watt lamp at the end of the line to light, we need to pump in 200 watts at the generator end!
Now lets say we redesign our lamp. We will keep it to be 100 watts, but design it with a higher resistance so it will operate from a higher voltage. Lets say we design it to work from 500 volts. so it has a resistance of 2500 ohms. We keep the conductors of the transmission line the same, so it still has a resistance of 100 ohms.
Say you have a 100 watt lamp, and you want to light it at the end of a long transmission line 100 kilometers long. Say the line has a resistance of 100 ohms.
Now you could design the lamp so that it runs from 100 volts. So to use 100 watts of electricity, it must have a resistance of 100 ohm (100 volts / 100 ohm = 1 amp, and then 100 volts x 1 amp = 100 watts).
but, becuase of the long transmision line, the generator at the end 'sees' not 1 ohm, but 200 ohms! To get 1 amp through the line to light the lamp, the generator must produce 1 amp x 200 ohms = 200 volts. The extra 100 volts is 'lost' in the resistance of the transmission line. Nopw since the transmission line is (in this example) just like a resistor, it will dissipate power just like the lamp (it will get warm). The power lost as heat will be 100 volts (voltage dropped across the resistance of the line) x 1 amp (current through the line) = 100 watts ! So we are only 50% efficient here, to get 100 watt lamp at the end of the line to light, we need to pump in 200 watts at the generator end!
Now lets say we redesign our lamp. We will keep it to be 100 watts, but design it with a higher resistance so it will operate from a higher voltage. Lets say we design it to work from 500 volts. so it has a resistance of 2500 ohms. We keep the conductors of the transmission line the same, so it still has a resistance of 100 ohms.
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