Power Transmission
Simple Explanation
Electrical power is transmitted over long distances at very HIGH voltage, specifically to keep the current LOW β since power lost as heat in the transmission lines is P_loss=I squared R, a lower current dramatically reduces wasted energy for the same delivered power.
Why Do We Need It?
This is exactly why power lines run at extremely high voltages (often hundreds of thousands of volts) β it is the single biggest lever for making a national electricity grid efficient rather than wasteful.
Formula
Power Loss in Transmission Lines
P_loss = IΒ²R
Transmitting power at a HIGHER voltage requires a proportionally LOWER current for the same delivered power β and since power lost as heat in the transmission lines grows with the square of current, high-voltage transmission dramatically reduces wasted energy.
- P_loss
- β power lost as heat in the transmission line, in watts (W)
- I
- β current flowing through the transmission line, in amperes (A)
- R
- β resistance of the transmission line, in ohms (Ξ©)
When to use it: Whenever the power wasted as heat in a transmission line needs to be found, or to compare the efficiency of transmitting the same power at different voltages.
Worked Example
Compare transmission losses at high and low voltage
A power station transmits 100000 W through a line of resistance 5 ohms. Compare the power lost at 10000 V versus 1000 V.
Why Does This Work?
Since power delivered is P=VI, transmitting the same power at ten times the voltage requires only one-tenth the current β and because power loss depends on the SQUARE of current (I squared R), reducing current by a factor of ten reduces the loss by a factor of one hundred, exactly as this comparison shows.
Real-Life Example
Why power lines are strung on tall towers at extremely high voltage
Long-distance electrical transmission lines often run at 100000 V or higher, requiring tall towers and heavy insulation for safety.
That very high voltage keeps the current (and therefore the wasted heat loss) as small as possible over the long distance, even though it demands more careful engineering for safe insulation.
Practice
A power station transmits 50000 W through a line of resistance 2 ohms at 5000 V. Find the power lost.
HardCommon mistake
Assuming power loss depends directly on voltage β it is actually the CURRENT that determines heat loss in the line; higher voltage is beneficial specifically because it REDUCES current for the same delivered power.
Quick Review
- P_loss = I squared R.
- Higher transmission voltage means lower current, means far less power lost.
- Halving current quarters the loss; a tenfold voltage increase gives a hundredfold loss reduction.