Answer to Question #117660 in Electric Circuits for Sam

Question

the mathematical comparisons of energy/power loss of transmitting electricity at different voltages

Answer 1

High voltages reduce the energy loss of power transmissions

Now, imagine that ta lamp needs 100W to operate. Let’s consider two ways to archieve this.

1. Let’s use very low voltage, 5V. The current needed to power a 100W lamp will be 100W / 5V = 20A.
2. Let’s use very high voltage, 500V. The current needed to power a 100W lamp will be 100W / 500V = 0.2A.

Now let’s assume that each wire has a constant resistance, equal to 0.01ohm, or 10 milliohms, which is a quite low, but still nonzero. Voltage drop across one wire, from Ohm’s law, will be: U = I × R.

1. In the first case (100W = 5V × 20A), voltage drop across one wire will be 20A × 0.01Ω = 0.2V. The power dissipated by this wire will be 0.2V × 20A = 4W, so transformer will need to supply 100W for the bulb + 8W for losses on two wires.
2. In the second case (100W = 500V × 0.2A), voltage drop across one wire will be 0.2A × 0.01Ω = 0.002V, or 2 mV. The power dissipated by this wire equals to 0.002V × 0.2A = 0.0004W, or 0.4 mW. Transformer needs to supply 100W for the bulb + 0.8 mW for losses.

What can we notice is that:

1. We increased the voltage 100 times (from 5V to 500V)
2. The current needed decreased 100 times (from 20A to 0.2A)
3. The voltage drop across the wire decreased 100 times (from 0.2V to 0.002V)
4. The power loss decreased 10000 (100 × 100) times