Calculator
Plotly Graph
The graph compares resistor current, inductor current, and total source current across a frequency sweep based on your present values.
Example Data Table
| Voltage (V RMS) | Frequency (Hz) | Resistance (Ω) | Inductance (H) | Xl (Ω) | Zeq (Ω) | Total Current (A) | Power Factor |
|---|---|---|---|---|---|---|---|
| 120.00 | 60.00 | 100.00 | 0.200 | 75.398 | 60.203 | 1.993 | 0.6020 Lagging |
| 230.00 | 50.00 | 120.00 | 0.350 | 109.956 | 81.069 | 2.837 | 0.6756 Lagging |
| 480.00 | 60.00 | 220.00 | 0.500 | 188.496 | 143.141 | 3.353 | 0.6506 Lagging |
Formula Used
An RL parallel circuit places the resistor and inductor across the same AC voltage source. Each branch sees identical voltage, but the currents differ in phase.
- Angular frequency: ω = 2πf
- Inductive reactance: Xl = ωL = 2πfL
- Resistor branch current: Ir = V / R
- Inductor branch current: Il = V / Xl
- Conductance: G = 1 / R
- Inductive susceptance magnitude: |Bl| = 1 / Xl
- Admittance magnitude: |Y| = √(G² + |Bl|²)
- Equivalent impedance magnitude: |Zeq| = 1 / |Y|
- Total current magnitude: It = √(Ir² + Il²)
- Phase angle: φ = -tan-1(Il / Ir)
- Power factor: cos(|φ|)
- Active power: P = V² / R
- Reactive power magnitude: Ql = V² / Xl
- Apparent power: S = V × It
The negative phase angle indicates a lagging current, which is expected in inductive networks.
How to Use This Calculator
- Enter the source voltage and choose whether it is RMS or peak.
- Provide the operating frequency and select the correct frequency unit.
- Enter the resistance value and choose the resistance unit.
- Enter the inductance value and choose the inductance unit.
- Set your preferred decimal precision for the output table.
- Click the calculate button to display results above the form.
- Review the graph to see how current changes with frequency.
- Use the CSV or PDF buttons to export the results.
About RL Parallel Circuits
An RL parallel circuit is a common AC network used in electrical analysis, controls, filtering, and power studies. The resistor branch consumes real power because its current stays in phase with the applied voltage. The inductor branch stores energy in a magnetic field and returns it later, so that branch mainly contributes reactive power and a lagging current component.
Because both elements sit in parallel, the applied voltage across each branch is identical. That makes branch current calculations straightforward once resistance and inductive reactance are known. The resistor current follows Ohm’s law directly. The inductor current depends on frequency, because inductive reactance rises as frequency increases. At higher frequencies, the inductor branch current drops, total current decreases, and the equivalent impedance usually rises.
Engineers often review admittance first in a parallel circuit. Conductance describes the real current path through the resistor, while susceptance describes the reactive path through the inductor. Combining these values gives total admittance, and the reciprocal gives equivalent impedance magnitude. This approach is practical for circuit design, maintenance work, and quick comparison between operating points.
The phase angle is also important. In an RL parallel network, total current lags the source voltage because the inductor branch current is ninety degrees behind the applied voltage. That lag produces a power factor below unity. Improving the power factor can reduce source current and improve system efficiency in larger installations.
This calculator helps you evaluate current distribution, impedance, power factor, and power quantities from one screen. It also adds export tools and a frequency sweep graph so you can document results, compare cases, and understand how the circuit behaves when operating conditions change.
Frequently Asked Questions
1. What does this RL parallel circuit calculator solve?
It solves inductive reactance, admittance, equivalent impedance, branch currents, total current, phase angle, power factor, and the main power quantities for an AC RL parallel network.
2. Why does the calculator ask for frequency?
Inductive reactance depends on frequency. When frequency changes, the inductor current changes, so total current, impedance, phase angle, and reactive power also change.
3. Can I enter peak voltage instead of RMS voltage?
Yes. Choose Peak in the voltage type field. The page converts peak voltage to RMS before calculating power, impedance, and current values.
4. Why is the phase angle negative?
The negative sign shows a lagging total current. In an inductive branch, current trails voltage, so the source current angle becomes negative in this calculator.
5. What happens when inductance increases?
Higher inductance raises inductive reactance at the same frequency. That reduces inductor current, often reduces total current, and can move the circuit toward a higher equivalent impedance.
6. Why is power factor less than one?
An ideal inductor introduces reactive current. That current increases apparent power without adding real power, so the power factor becomes lower than unity.
7. Does this tool work for DC circuits?
No. This page is intended for AC steady state analysis. It requires a frequency above zero because reactance and phase relationships depend on AC operation.
8. What can I export from the page?
You can export the calculated result table as CSV for spreadsheet work or as PDF for reports, quotations, documentation, and field records.