RL Circuit Inputs
Choose a solving mode, enter known values, and leave unrelated fields unchanged.
How to use this calculator
- Select a DC transient, AC steady-state, or reverse-solving mode.
- Enter each known electrical value and select its matching unit.
- Use initial current for transient calculations when the inductor is not starting from zero.
- Choose decimal precision, then press the calculation button.
- Review the result cards, formulas, substitutions, graph, and detailed table.
- Copy the result or export the calculation as CSV or PDF.
Example data
| Mode | Resistance | Inductance | Voltage | Frequency or time | Expected focus |
|---|---|---|---|---|---|
| DC energizing | 100 Ω | 0.5 H | 12 V | 0.01 s | Current rise and time constant |
| DC de-energizing | 47 Ω | 220 mH | 0 V | 5 ms | Current decay from initial current |
| Series RL AC | 100 Ω | 0.5 H | 120 V RMS | 60 Hz | Impedance, phase, and power |
| Parallel RL AC | 220 Ω | 150 mH | 24 V RMS | 50 Hz | Branch currents and equivalent impedance |
Understanding RL circuits
An RL circuit combines resistance and inductance. The resistor immediately opposes current according to Ohm’s law. The inductor opposes changes in current by producing a counter voltage.
During DC energizing, current rises exponentially instead of changing instantly. The time constant equals inductance divided by resistance. After five time constants, current is very near its final value.
During de-energizing, stored magnetic energy keeps current flowing temporarily. Current then decays exponentially toward zero. The inductor voltage reverses polarity while releasing stored energy safely.
For sinusoidal AC, the inductor contributes reactance. Reactance increases with frequency and inductance. This causes current to lag voltage in a series RL circuit.
In a parallel RL circuit, resistor current stays aligned with voltage. Inductor current lags voltage by ninety degrees. Total current is the vector sum of both branch currents.
Real power is consumed by resistance. Reactive power circulates through the inductor. Apparent power combines real and reactive power through vector relationships.
Power factor describes how effectively apparent power becomes useful real power. A stronger inductive effect lowers the power factor. Increasing resistance can reduce the phase difference in series circuits.
Stored magnetic energy depends on inductance and current squared. Doubling current increases stored energy four times. Proper switching protection is important when interrupting inductive current.
Reverse-solving modes are useful during component selection. They can determine resistance, inductance, frequency, time, voltage, or current. Always confirm practical ratings after completing theoretical calculations.
Real inductors include winding resistance and parasitic capacitance. Core saturation and heating can also change behavior. Therefore, measured results may differ from ideal calculations in practice.
Frequently asked questions
What is an RL circuit?
It is a circuit containing resistance and inductance. The components may be connected in series or parallel.
What does the RL time constant represent?
It measures how quickly current changes. One time constant equals inductance divided by resistance.
Why does inductor current not change instantly?
An instantaneous current change would require infinite voltage. The inductor generates voltage opposing rapid current changes.
What happens after five time constants?
An energizing current is above ninety-nine percent of its final value. A decaying current is below one percent.
What is inductive reactance?
Inductive reactance is AC opposition caused by inductance. It equals two times pi times frequency times inductance.
Does current lead or lag in an RL circuit?
Current lags source voltage in a series RL circuit. The lag depends on resistance and inductive reactance.
How is series RL impedance calculated?
Treat resistance and reactance as perpendicular components. The magnitude is the square root of their squared sum.
How are parallel RL currents combined?
Resistor and inductor branch currents are ninety degrees apart. Combine them using vector addition.
Can this calculator determine a missing component?
Yes. Reverse modes solve resistance, inductance, frequency, transition time, voltage, and current from stored energy.