Inductor Calculator (X_L, Energy, Time Constant)
Inductors store energy in magnetic fields and resist changes in current. They are found in power supplies, filters, motors, and radio circuits. This calculator gives you the three most important inductor properties: reactance (how much it opposes AC current), stored energy, and the RL time constant that controls how fast current ramps up.
Key Inductor Formulas
Inductive Reactance
X_L = 2 pi f L
Reactance is the inductor's opposition to alternating current. Unlike resistance, reactance increases with frequency. A 10 mH inductor has 6.28 ohms of reactance at 100 Hz but 62.8 ohms at 1 kHz. This frequency-dependent behavior is what makes inductors useful as filters.
Stored Energy
E = 1/2 L I squared
An inductor carrying current stores energy in its magnetic field, just like a capacitor stores energy in its electric field. A 10 mH inductor carrying 5A stores 125 mJ. This energy gets released when the current is interrupted, which can create voltage spikes.
RL Time Constant
tau = L / R
When you apply voltage to an RL circuit, the current does not jump instantly. It rises exponentially with time constant tau = L/R. After one time constant, current reaches 63.2% of its final value. After five time constants (5 tau), it is effectively at full value (99.3%).
Impedance in an RL Circuit
When an inductor is in series with a resistor: Z = sqrt(R squared + X_L squared)
| Inductance | Frequency | X_L | With 100 ohm R: Z |
|---|---|---|---|
| 10 mH | 100 Hz | 6.28 ohms | 100.2 ohms |
| 10 mH | 1 kHz | 62.8 ohms | 118.1 ohms |
| 10 mH | 10 kHz | 628 ohms | 636 ohms |