RL Circuit Calculator

Circuit Inputs

Mode

Resistance (Ω)

Inductance (H)

Supply Voltage (V)

Time t (s)

Initial Current (A)

Target Current Fraction

Use current growth for switch-on analysis. Use current decay for switch-off analysis.

Transient Plot

Example Data Table

Case	R (Ω)	L (H)	V (V)	Mode	τ = L/R (s)	Steady Current (A)
Lab Coil A	10	0.5	24	Growth	0.0500	2.4000
Motor Winding	8	0.2	12	Growth	0.0250	1.5000
Relay Release	15	0.3	0	Decay	0.0200	0.0000

Formula Used

Time constant: τ = L / R

Steady-state current: I∞ = V / R

Growth current: i(t) = I∞ + (I₀ - I∞)e^-t/τ

Decay current: i(t) = I₀e^-t/τ

Current rate change: di/dt = derivative of i(t)

Resistor voltage: V_R = iR

Inductor voltage: V_L = L(di/dt)

Stored magnetic energy: E = 0.5Li²

An RL circuit opposes sudden current change because the inductor stores magnetic energy. The time constant tells you how fast the current rises or falls.

How to Use This Calculator

Choose current growth or current decay mode.
Enter resistance and inductance values using consistent units.
Enter source voltage for growth analysis.
Enter the observation time where you want results.
Provide initial current when analyzing stored current effects.
Set a target current fraction for timing estimates.
Press the calculate button to show values above the form.
Review the graph, then export the results as CSV or PDF.

Frequently Asked Questions

1. What does an RL circuit calculator compute?

It computes time constant, current, current slope, resistor voltage, inductor voltage, energy storage, steady current, and time to reach a selected current fraction.

2. What is the time constant in an RL circuit?

The time constant is τ = L/R. It shows how quickly current changes. After one time constant, growth current reaches about 63.2% of its final value.

3. Why does inductor voltage decrease during current growth?

At switching, the inductor strongly opposes current change. As current approaches steady state, the rate of change becomes smaller, so inductor voltage drops.

4. What happens during current decay?

When the source is removed, stored magnetic energy drives current through the resistor. The current then decreases exponentially toward zero.

5. Why is resistance important in transient response?

Higher resistance reduces the time constant because τ = L/R. That means the circuit reaches its final or near-zero current faster.

6. Why is inductance important in transient response?

Higher inductance increases the time constant. The circuit then resists current change more strongly, causing slower current rise and slower decay.

7. Can I use this for coils, relays, and motor windings?

Yes. This calculator is useful for practical RL loads such as coils, solenoids, relay windings, electromagnets, and some motor winding approximations.

8. What units should I use?

Use ohms for resistance, henries for inductance, volts for source voltage, seconds for time, amperes for current, and joules for stored energy.