- 1). Equate the two coils' magnetic fields. Recall that a solenoid with current i and n turns has a magnetic field in the center of B=μin, where μ is the magnetic permeability constant. Equating the two magnetic fields gives you the first equation mentioned in the introduction above.
- 2). Equate the power flowing through both coils. According to the principle of conservation of energy, the power, or rate of energy transfer, has to be equal between the two coils if only a negligible amount is lost in the transformer as heat (a reasonable assumption usually). Electrical power through a P equals iV, where V is the potential drop across the coil. P is the same for both coils, so i_1 x V_1 = i_2 x V_2--the second equation in the introduction.
- 3). Combine these two equations to derive a third equation that directly relates coil turns with the voltage difference between circuits. In other words, n_2 / n_1 = i_1 / i_2 = V_2 / V_1. Therefore, n_2 / n_1 = V_2 / V_1. So for example, if you want to step down the voltage from one circuit to another--from, say, 110V down to 12V--you'll have the energy-delivering circuit have 110/12 times as many turns around the transformer as the receiving circuit makes.
SHARE
