Find out why transmission voltages are raised to hundreds of thousands of volts, and explore the physics behind power generation and everyday technology.
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送出電力と送電線の抵抗が一定なら、送出電圧10倍で損失は何倍か？
電流100 Aと抵抗が一定なら、送出電圧10倍で損失は何倍か？
Equations explain the phenomenon.
1Transmitted power is expressed in terms of voltage and electric current.P=V I……
2The electric current is calculated from the power and voltage.I=PV……
3Substituting the expression for electric current gives the transmission loss in terms of voltage.Ploss=R(PV)²……
The discussion extends to power generation and everyday technology.
4Conservation of energy extends to heat and atomic nuclei.Etotal=Constant……
5The energy in fuel is traced through a thermal power station.Electricity≒Fuel × 0.41……
6Temperatures determine the upper limit on heat engine efficiency.e≦1 − TlowThigh……
7A rotating coil produces a voltage in a generator.V=B S ω sin ωt……
8The energy released by nuclear fission in 1 g of uranium is calculated.1 g of 235U→8.2×10¹⁰ J……
9Sunlight is converted into electricity without a heat engine.Solar constant=1361 W/m²……
The symbols used in the GPS equation in the next step are defined as follows: G is the universal gravitational constant, M is the mass of Earth, r is the distance from Earth's center to the satellite, and REarth is Earth's radius (a different symbol from the resistance R of a transmission line).
10The satellite clock shifts predicted by the 2 theories of relativity are added together.Δt=-7.2 +45.7=+38.5 μsday……
11An electron energy difference determines the wavelength of the emitted light.λ=h cEg……
12Spacetime distortion is measured through changes in the difference between arm lengths.ΔLL≒10⁻²¹……
What this chapter has shown
If the transmitted power P=VI and transmission line resistance R remain unchanged, increasing the transmission voltage by a factor of n reduces the electric current to 1/n of its original value. Since the transmission loss RI² is proportional to the square of the electric current, it falls to 1/n² of its original value.
0.010 times the original valuePower and resistance remain constant; voltage increases by a factor of 10
However, if the electric current and resistance remain constant, increasing the transmission voltage leaves the loss RI² unchanged.
In everyday lifeThe gray cylinders on utility poles are transformers that lower 6600 V to 100 V or 200 V.
Detailed summary
For a given transmitted power, increasing the transmission voltage reduces the electric current, and the transmission loss RI² decreases with the square of the electric current. This is why electricity is transmitted at high voltages. Energy is conserved as it changes form, but converting heat into work always requires some heat to be rejected. Electricity generation relies on electromagnetic induction, while nuclear power relies on the relationship between mass and energy. Both can be analyzed quantitatively using the physics covered in earlier chapters. New technologies, such as GPS, LEDs, and gravitational wave detection, build on the physics that began with the equation of motion.