Define the resistance from Hertz, or Hz, application. In this example, a standard inductive coil in a nonreactive industrial power control system application normally passes 800-watts of power at 240-volts AC and 60 Hz. If a researcher wants to use the same coil to limit current flow at 120 Hz, or twice the frequency, you can calculate the new dynamic resistance or impedance value of the coil, and the amount of power it allows to pass.
Calculate the current in amperes, or amps, flowing when the frequency is 60 Hz. For nonreactive loads, power in watts = volts * amps and therefore, amps = watts/volts. Substituting stated values, current in amps = 800 watts/240 volts = 3.333 amps. Since the inductor formula is X(inductor) = V volts/I amps, then X(inductor) = 240/3.333 = 72 ohms.
Determine the inductor's value in Henries (H) and millihenries (mH). Since X(inductor) = w(angular frequency in radians/sec) * L(inductance in millihenries), then L = X/w where w = 2 * pi * frequency (Hz) or 2 * 3.1416 * 60 hz = 377 radians/second. Substituting calculated values, L = 72 ohms/377 radians/sec = 0.191 Henries or 191 millihenries.
Calculate the new value of X if frequency is doubled to 120 Hz. This effectively doubles the value of w in radians/second from 377 to 754. Now X = 754 radians/second * 0.191 Henries = 144 ohms of impedance.
Calculate resistance from the new value of impedance, 144 ohms. Because the load is nonreactive, resistance R in ohms = X = 144 ohms at the higher frequency.
Calculate the new value of power in watts at the higher frequency by solving I = V/X, = 240 volts/144 ohms = 1.667 amps. Power = V * I or 240 * 1.667 or 400 watts of power that will be passed by the inductor.
Things You Will Need
- Scientific calculator
- Check the DC resistance of an inductor first to see if it will overheat with lower frequencies.