Inductor Energy & Time Constant Calculator
Calculate energy stored in an inductor, L/R time constant, and current rise time
Formula
E = ½LI², τ = L/R, i(t) = I_final × (1 - e^(-t/τ))
How It Works
Inductors are passive electronic components that store energy in their magnetic field when current flows through them. The energy storage capability of an inductor is described by the equation E = ½LI², where E represents stored energy in joules, L is inductance in henries, and I is current in amperes. The time constant (τ) for an inductor circuit is determined by the ratio of inductance (L) to resistance (R), which governs the rate of current change and energy buildup in the circuit. During energization, an inductor resists sudden current changes, creating a nonlinear charging profile where current rises exponentially according to the equation I(t) = I_max(1 - e^(-t/τ)). This behavior is critical in power supply design, filtering, and energy storage applications.
Worked Example
Consider a 10 mH inductor with a 5 Ω resistor and a maximum current of 2 A. The time constant (τ) would be calculated as L/R = 10 mH / 5 Ω = 2 ms. The stored energy at peak current is E = ½ * 0.01 H * (2 A)² = 0.02 joules. The rise time to 63% of maximum current would be approximately one time constant (2 ms), reaching about 1.26 A in that duration. This demonstrates how inductors smoothly manage current transitions in electronic systems.
Practical Tips
- ✓Always consider inductor's internal resistance when calculating time constants
- ✓Use core material specifications to understand saturation limits
- ✓Verify actual inductor performance with oscilloscope measurements
Common Mistakes
- ✗Neglecting inductor resistance when calculating time constants
- ✗Assuming linear current rise instead of exponential
- ✗Ignoring saturation effects in real inductors
Frequently Asked Questions
What does the time constant represent in an inductor circuit?
The time constant represents the duration required for the current to reach approximately 63.2% of its maximum value during charging or discharging.
How does inductor size affect energy storage?
Larger inductance values and higher currents increase energy storage capacity quadratically according to the E = ½LI² equation.
Can inductors store energy indefinitely?
No, inductors will eventually dissipate stored energy through resistance and core losses over time.
How do you calculate maximum stored energy?
Calculate stored energy by multiplying ½ times inductance times the square of maximum current.
What factors limit an inductor's performance?
Core saturation, DC resistance, temperature, and maximum current rating are primary performance limitations.
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