Calculate RLC Parallel Circuit

Calculator and formulas for calculating voltage and power of an RLC parallel circuit

Calculate RLC Parallel Circuit

RLC Parallel Circuit

This function calculates power, current, impedance and reactance of a parallel circuit consisting of resistor, inductor and capacitor at a given frequency.

Results
Reactance XL:
Reactance XC:
Total impedance Z:
Current through inductor IL:
Current through capacitor IC:
Current through resistor IR:
Total current I:
Active power P:
Reactive power QL:
Reactive power QC:
Apparent power S:
Phase angle φ:

RLC Parallel Circuit

LCR Parallel Circuit, RLC Parallel Circuit
Parallel Circuit Properties
  • Same voltage across all components
  • Geometric addition of branch currents
  • IL and IC are 180° out of phase
  • Total current can be smaller than largest branch current
Basic Formulas
\[I=\sqrt{I_R^2+(I_C-I_L)^2}\] \[Y=\sqrt{G^2+(B_C-B_L)^2}\]

Current and admittance triangle according to Pythagoras

Admittances
  • G: Conductance = 1/R
  • BL: Inductive susceptance = 1/XL
  • BC: Capacitive susceptance = 1/XC
  • Y: Admittance = 1/Z

RLC Parallel Circuit - Theory and Formulas

Fundamentals of RLC Parallel Circuit

The total resistance of the RLC parallel circuit in the AC circuit is called impedance Z. Ohm's law applies to the complete circuit. The total current I is the sum of the geometrically added branch currents.

Current Triangle

Currents
\[I=\sqrt{I_R^2+(I_C-I_L)^2}\]
IL = Current through the inductor
IC = Current through the capacitor
IR = Current through the resistor
I = Total current
Admittance Triangle
\[Y=\sqrt{G^2+(B_C-B_L)^2}\]
Y = Admittance
G = Conductance
BL = Inductive susceptance
BC = Capacitive susceptance

Reactances and Currents

Reactances
\[X_L = 2\pi f L\] \[X_C = \frac{1}{2\pi f C}\]

Frequency-dependent resistances of inductor and capacitor.

Branch Currents
\[I_R = \frac{U}{R}\] \[I_L = \frac{U}{X_L}\] \[I_C = \frac{U}{X_C}\]

All branches have the same voltage U.

Total Current
\[I = \frac{U}{Z}\]

Geometric addition of branch currents.

Power Triangle

Powers
\[S=\sqrt{P^2+(Q_C-Q_L)^2}\]
\[P = I_R \cdot U\] \[Q_L = I_L \cdot U\] \[Q_C = I_C \cdot U\]
P = Active power, S = Apparent power
QL = Inductive reactive power, QC = Capacitive reactive power

Phase Relationships

Phase Positions
\[\phi = \arccos\left(\frac{R}{Z}\right)\]
  • Resistor R: Current and voltage in phase
  • Inductor L: Voltage leads current by +90°
  • Capacitor C: Voltage lags current by -90°
  • Resulting phase: Depends on IC - IL

Frequency Behavior

Low Frequencies
  • XC >> XL
  • IC << IL
  • Inductive behavior
  • Positive phase shift
Resonance Frequency
  • IL = IC
  • Z = R (maximum)
  • φ = 0°
  • Minimum total current
High Frequencies
  • XL >> XC
  • IL << IC
  • Capacitive behavior
  • Negative phase shift

Practical Applications

Filter circuits:
• Band-stop filters
• Parallel resonant circuits
• Interference suppression
• Crossover networks
Tuned circuits:
• Tank circuits
• Oscillator circuits
• Antenna tuners
• Resonant circuits
Reactive power:
• Compensation
• Power factor
• Energy storage
• Impedance matching

Differences to Series Circuit

Parallel vs. Series
Parallel circuit:
  • Same voltage across all components
  • Z maximum at resonance
  • I minimum at resonance
  • Current division according to impedance
Series circuit:
  • Same current through all components
  • Z minimum at resonance
  • I maximum at resonance
  • Voltage division according to impedance

Design Guidelines

Important Design Aspects
  • Current division: Depends on frequency and component values
  • Resonance: At f₀ = 1/(2π√LC), Z is maximum
  • Current enhancement: IL and IC can significantly exceed I
  • Losses: ESR of components reduces maximum impedance
  • Loading: Additional parallel load reduces total impedance
  • Quality factor: Q = R/(XL or XC) at resonance

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