To create a “frequency to power” calculator, it’s important to understand that the conversion isn’t straightforward, as frequency (measured in Hertz, Hz) and power (measured in watts, W) describe different physical quantities.
However, in specific contexts, such as radio transmissions or audio systems, it’s possible to link frequency-related parameters to power calculations through the inclusion of additional data such as signal amplitude, impedance, or system efficiency.
Enter
- Frequency (use the dropdown menu to select the units – Hz, kHz, MHz )
- Inductance value
- Current through the inductor in Amps
The tool will calculate the power in Watt
Formula
For a pure inductor, the impedance (ZL) can be represented as:
ZL= jωL = j2πfL
The reactance is given by XL= ωL = 2πfL
Power in watt is P = I2⋅XL
Where:
- ZL is the impedance of the inductor.
- j is the imaginary unit (to denote the 90-degree phase shift between voltage and current in an inductor).
- ω is the angular frequency of the AC signal (measured in radians per second).
- L is the inductance of the inductor (measured in Henry).
- I is the current
In this representation, the magnitude of the impedance ZL is directly proportional to the frequency of the AC signal (ω) and the inductance (L).
Note that the units for reactance are ohm and the impedance is an imaginary quantity with the same absolute value and units.
Example Calculation
Assume an inductor with L = 1 H, frequency f = 50 Hz, and an RMS current I=2 A flowing through it. At a frequency of 50 Hz the Power is calculated to be approximately 1256 Watt.
This calculation shows the power associated with the inductive reactance, but remember, this isn’t the “power consumed” by the inductor in the usual sense because ideal inductors do not dissipate energy. Instead, this calculation reflects the power handling due to the inductor’s impedance in the circuit.
As the frequency increases, the power handling increases as well.