Wednesday 7-23-96
Electricity is often generated quite a long way from where it is used, so it is often transmitted long distances through power lines. Although the resistance of a power line is relatively low, over long distances it can add up to quite substantial values. A power line of resistance R causes a power loss of I^2 R; this is wasted as heat. By reducing the current, therefore, the I^2 R losses can be minimized. Because power is given by P = VI, to reduce the current the voltage is increased (conserving power amounts to the same thing as conserving energy).
Using AC power, and Faraday's law of induction, there is a very simple way to increase voltage and decrease current (or vice versa), and that is to use a transformer. A transformer is made up of two coils, linked so the magnetic flux from one passes through the other. When the flux generated by one coil changes (as it does continually if the coil is connected to an AC power source), the flux passing through the other will change, inducing a voltage in the second coil. With AC power, the voltage induced in the second coil will also be AC.
In a standard transformer, the two coils are usually wrapped around the same iron core, which ensures that the magnetic flux is the same through both coils. The coil that provides the flux (i.e., the coil connected to the AC power source) is known as the primary coil, while the coil in which voltage is induced is known as the secondary coil. If the primary coil sets up a changing flux, the voltage Vs in the secondary coil depends on the number of turns Ns in the secondary:
Similarly, the relationship for the primary coil, with Np turns, is:
Combining these gives the relationship between the primary and secondary voltage:
Vs/Vp = Ns/Np
Energy (or, equivalently, power) has to be conserved, and the power is given by P = VI. Therefore P = VsIs = VpIp.
So, Vs/Vp = Ns/Np = Ip/Is
If a transformer takes a high primary voltage and converts it to a low secondary voltage, the current in the secondary will be higher than that in the primary to compensate (and vice versa). A transformer in which the voltage is higher in the primary than the secondary (i.e., more turns in the primary than the secondary) is known as a step-down transformer. A transformer in which the opposite is true, in which the secondary has more turns (and, therefore, higher voltage) is known as a step-up transformer.
Power companies use step-up transformers to boost the voltage to hundreds of kV before it is transmitted down a power line, thereby reducing the current and preventing the loss of large amounts of power in the lines. Step-down transformers are used at the other end, to decrease the voltage level down to the 120 - 240 V used in household circuits.
Note that transformers require a varying flux in order to work. They are therefore perfect for use with AC power; on the other hand, they would not work at all for DC power, which would keep the flux constant. The ease with which voltage and current can be tranformed in an AC circuit is a large part of the reason AC power, rather than DC, is distributed by the power companies.
We can extend the parallel between fluids and electricity (such as by comparing a current flowing through a circuit to water flowing through pipes) by comparing transformers to hydraulics. A hydraulic lift, for example, can raise a car in a service station through conservation of energy; by applying a relatively small pressure to a large area, a large pressure (enough to lift a car) can be generated in a small area. A transformer does a similar job, taking a small voltage (pressure) and transforming it to a high voltage (or vice versa), conserving energy by reducing the current to compensate.