RLC parallel circuit calculation

The calculator calculates the voltages, powers, currents, impedance and reactance in the parallel circuit of a resistor of a inductor and a capacitor.

Formulas for RLC parallel circuit

The total resistance of the RLC series circuit in an AC circuit is as Impedance Z denotes. Ohm's law applies to the entire circuit.

• Current and voltage are in phase at the ohmic resistance.

• At the inductive reactance of the coil, the voltage leads the current by + 90 °.

• At the capacitive reactance of the capacitor, the voltage lags the current by -90 °.

• Therefore U_L and U_C are out of phase by 180 °.

The total current I is the sum of the geometrically added partial currents.

For this purpose, the current at the resistor forms the leg of a right triangle. The other cathede is the difference between the currents I_L and I_C , since these are out of phase. The hypotenuse corresponds to the total current I.

The resulting triangle is called the current triangle or vector diagram of the currents.

Current triangle

\(\displaystyle I=\sqrt{ {I_R}^2 + (I_C-I_L)^2} \)

\(\displaystyle I_L\)	Current through the inductor
\(\displaystyle I_C\)	Current through the capacitor
\(\displaystyle I_R\)	Current through the resistor
\(\displaystyle I\)	Total current

Conductance triangle

\(\displaystyle Y=\sqrt{G^2 + (B_L-B_C)^2} \)

\(\displaystyle Y\)	Admittance
\(\displaystyle G\)	Real conductance
\(\displaystyle B_L\)	Inductive susceptance
\(\displaystyle B_C\)	Capacitive susceptance

Power triangle

\(\displaystyle S=\sqrt{P^2 + (Q_L-Q_C)^2} \)

\(\displaystyle P\)	Real power
\(\displaystyle S\)	Apparent power
\(\displaystyle Q_L\)	Inductive reactive power
\(\displaystyle Q_C\)	Capacitive reactive power

More formulas

Current
\(\displaystyle I=\frac{U}{Z} \)	\(\displaystyle I_R=\frac{U}{R} \)	\(\displaystyle I_L=\frac{U}{X_L} \)	\(\displaystyle I_C=\frac{U}{X_C} \)

Resistor
\(\displaystyle X_L=2π · f · L \)	\(\displaystyle X_C=\frac{1}{2π · f · C} \)

Power
\(\displaystyle P=I·U_R \)	\(\displaystyle Q_L=I·U_L \)	\(\displaystyle Q_C=I·U_C \)

Phase
\(\displaystyle φ = acos\left(\frac{Z}{R}\right) \)