Calculator and formulas for calculating resistor and inductor in parallel
The computer calculates the voltages, power, current, impedance and reactance for a resistor and inductor in parallel.

\(\displaystyle I\) Total current \(\displaystyle I_R\) Current through the resistor \(\displaystyle I_L\) Current through the coil \(\displaystyle Y\) Admittance [1/Z] \(\displaystyle X_L\) Inductive reactance \(\displaystyle R\) Effective resistance \(\displaystyle Z\) Impedance \(\displaystyle G\) Conductance [1/R] \(\displaystyle B_L\) Susceptance [1/X_{L}] \(\displaystyle P\) Real power \(\displaystyle S\) Apparent power \(\displaystyle Q_L\) Inductive reactive power \(\displaystyle φ\) Phase shift in °
The total resistance of the RL parallel circuit in AC is called impedance Z. Ohm's law applies to the entire circuit.
Current and voltage are in phase at the ohmic resistance. The inductive reactance of the capacitor lags the current the voltage by −90 °.
The total current I is the sum of the geometrically added partial currents. For this purpose, both partial flows form the legs of a right triangle. Its hypotenuse corresponds to the total current I. The resulting triangle is called the current triangle or vector diagram of the currents.
\(\displaystyle I=\sqrt{ {I_R}^2+{I_L}^2} \) \(\displaystyle =\frac{U}{Z} \) \(\displaystyle I_R=\sqrt{I^2{I_L}^2} \) \(\displaystyle =\frac{U}{R} \) \(\displaystyle =I·cos(φ) \) \(\displaystyle I_L=\sqrt{I^2{I_R}^2} \) \(\displaystyle =\frac{U}{X_L} \) \(\displaystyle =I·sin(φ) \)
When connected in parallel, the partial currents behave like the conductance values of resistances.
\(\displaystyle Y=\sqrt{G^2+{B_L}^2} \) \(\displaystyle =\frac{1}{Z} \) \(\displaystyle G=\sqrt{Y^2{B_L}^2} \) \(\displaystyle =\frac{1}{R} \) \(\displaystyle B_L=\sqrt{Y^2G^2} \) \(\displaystyle =\frac{1}{X_L} \) \(\displaystyle φ=\frac{B_L}{G} \)
\(\displaystyle Z=\frac{R· X_L}{\sqrt{R^2+{X_L}^2}} \) \(\displaystyle =\frac{1}{Y}\) \(\displaystyle R=\frac{Z· X_L}{\sqrt{Z^2{X_L}^2}} \) \(\displaystyle =\frac{1}{G}\) \(\displaystyle X_L=\frac{Z· R}{\sqrt{Z^2R^2}} \) \(\displaystyle =\frac{1}{B_L}\)
\(\displaystyle S=\sqrt{P^2+{Q_L}^2} \) \(\displaystyle =U·I \) \(\displaystyle P=\sqrt{S^2{Q_L}^2} \) \(\displaystyle =U_R·I_R \) \(\displaystyle Q_L=\sqrt{S^2P^2} \) \(\displaystyle =U_L·I_L \)
\(\displaystyle cos(φ)=\frac{P}{S}=\frac{I_R}{I}\)
