Calculator Inputs
Large: 3 columns · Medium: 2 · Mobile: 1Example Data Table
This sample shows a common RL step response setup for testing the solver.
| Mode | Source Voltage (V) | Resistance (Ω) | Inductance (H) | Initial Current (A) | Time | Target Current (A) |
|---|---|---|---|---|---|---|
| Step response | 24 | 12 | 0.6 | 0 | 0.08 s | 1.5 |
| Natural decay | 0 | 8 | 0.4 | 2.2 | 60 ms | 0.5 |
Formula Used
Series RL differential equation: L(di/dt) + Ri = Vs
Time constant: τ = L / R
Current response: i(t) = If + (I0 − If)e−t/τ
Final current: If = Vs / R
Resistor voltage: VR = Ri(t)
Inductor voltage: VL = Vs − Ri(t)
Current slope: di/dt = (Vs − RI0)e−t/τ / L
Stored energy: W = ½Li(t)2
Time to target current: t = −τ ln[(Itarget − If) / (I0 − If)]
The solver applies the standard closed-form RL response. For natural decay, the source voltage becomes zero, so current falls exponentially from the initial value.
How to Use This Calculator
- Select Step response for a powered RL circuit or Natural decay for source-free current decay.
- Enter resistance, inductance, initial current, and the evaluation time. Add a target current if you also want the required time.
- Choose seconds or milliseconds, then click Solve Circuit. The results will appear above the form.
- Review the summary metrics, target timing check, and the response table that spans from 0 to 5 time constants.
- Use the export buttons to download the current result block as CSV or PDF for analysis, reports, or records.
Frequently Asked Questions
1. What does this solver calculate?
It calculates time constant, current, resistor voltage, inductor voltage, current slope, stored magnetic energy, power, and the time needed to hit a target current.
2. What is the time constant in an RL circuit?
The time constant equals inductance divided by resistance. It shows how quickly current rises or decays. After about five time constants, the response is very close to its final value.
3. When should I use natural decay mode?
Use natural decay when the source is removed and the inductor current decreases through the resistor. The solver then treats source voltage as zero and models exponential decay.
4. Why might the target current be unreachable?
A target is unreachable when it lies outside the actual response path. For example, a rising current cannot cross a target below both its starting and final levels.
5. Why does the inductor voltage decrease over time?
As current approaches its final value, the rate of change becomes smaller. Because inductor voltage depends on current change, the voltage across the inductor decays toward zero.
6. Can I use milliseconds for time input?
Yes. Choose milliseconds in the time unit field, and the solver converts the value internally to seconds before computing the response and target timing.
7. What does the response table represent?
The response table samples the circuit from zero to five time constants. This range is useful because it captures the most important part of the transient behavior.
8. Do the export buttons save both summary and table data?
Yes. The CSV and PDF exports include the main results and the sampled response table, making it easier to share or archive calculated outputs.