Resistor and inductor in parallel

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.

RL in parallel calculator

Input

Coil

Resistor

Frequency

Voltage

Decimal places

Results

Resistance XL

Impedance Z

Current in resistor I_R

Current in the coilI_L

Current I

Real power P

Reactive power Q

Apparent power S

Phase angle φ

I Total current

I_R Current through the resistor

I_L Current through the coil

Y Admittance [1/Z]

X_L Inductive reactance

R Effective resistance

Z Impedance

G Conductance [1/R]

B_L Susceptance [1/X_L]

P Real power

S Apparent power

Q_L Inductive reactive power

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

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

Other induction calculators

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Reactance of a coil
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Lowpass filter R/L
Series circuit R/L
Parallel circuit R/L
Transformer

I	Total current
I_R	Current through the resistor
I_L	Current through the coil
Y	Admittance [1/Z]
X_L	Inductive reactance
R	Effective resistance
Z	Impedance
G	Conductance [1/R]
B_L	Susceptance [1/X_L]
P	Real power
S	Apparent power
Q_L	Inductive reactive power
φ	Phase shift in °

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

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

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

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