# Resistor and inductor in parallel

Calculator and formulas for calculating resistor and inductor in parallel

## Calculate resistor and inductor in parallel

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

RL in parallel calculator

 Input Coil H mH µH nH Resistor mΩ Ω kΩ MΩ Frequency Hz kHz MHz GHz Voltage mV V kV Decimal places 0 1 2 3 4 6 8 10 Results Resistance XL Impedance Z Current in resistor IR Current in the coilIL Current I Real power P Reactive power Q Apparent power S Phase angle φ

 $$\displaystyle I$$ 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/XL] $$\displaystyle P$$ Real power $$\displaystyle S$$ Apparent power $$\displaystyle Q_L$$ Inductive reactive power $$\displaystyle φ$$ Phase shift in °

## Formulas and description for RL in parallel

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.

### Current triangle

 $$\displaystyle I=\sqrt{ {I_R}^2+{I_L}^2}$$ $$\displaystyle =\frac{U}{Z}$$ $$\displaystyle I_R=\sqrt{I^2-{I_L}^2}$$ $$\displaystyle =\frac{U}{R}$$ $$\displaystyle =I·cos(φ)$$ $$\displaystyle I_L=\sqrt{I^2-{I_R}^2}$$ $$\displaystyle =\frac{U}{X_L}$$ $$\displaystyle =I·sin(φ)$$

### Conductance triangle

When connected in parallel, the partial currents behave like the conductance values of resistances.

 $$\displaystyle Y=\sqrt{G^2+{B_L}^2}$$ $$\displaystyle =\frac{1}{Z}$$ $$\displaystyle G=\sqrt{Y^2-{B_L}^2}$$ $$\displaystyle =\frac{1}{R}$$ $$\displaystyle B_L=\sqrt{Y^2-G^2}$$ $$\displaystyle =\frac{1}{X_L}$$ $$\displaystyle φ=\frac{B_L}{G}$$

### Resistance triangle

 $$\displaystyle Z=\frac{R· X_L}{\sqrt{R^2+{X_L}^2}}$$ $$\displaystyle =\frac{1}{Y}$$ $$\displaystyle R=\frac{Z· X_L}{\sqrt{Z^2-{X_L}^2}}$$ $$\displaystyle =\frac{1}{G}$$ $$\displaystyle X_L=\frac{Z· R}{\sqrt{Z^2-R^2}}$$ $$\displaystyle =\frac{1}{B_L}$$

### Power triangle

 $$\displaystyle S=\sqrt{P^2+{Q_L}^2}$$ $$\displaystyle =U·I$$ $$\displaystyle P=\sqrt{S^2-{Q_L}^2}$$ $$\displaystyle =U_R·I_R$$ $$\displaystyle Q_L=\sqrt{S^2-P^2}$$ $$\displaystyle =U_L·I_L$$

### Power factor

$$\displaystyle cos(φ)=\frac{P}{S}=\frac{I_R}{I}$$

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