Parallel RL Circuit Impedance Calculator

Formulas Used in Calculations

For a parallel RL circuit, where:

• \(f\) = Frequency in Hertz (Hz)
• \(\omega = 2\pi f\) = Angular frequency in radians per second (rad/s)
• \(X_L = \omega L\) = Inductive reactance in ohms (Ω)

The impedance of the inductor is given by:

\(Z_L = j\omega L\)

The equivalent impedance \(Z\) of the parallel RL circuit is:

\(\dfrac{1}{Z} = \dfrac{1}{R} + \dfrac{1}{Z_L}\)

Which simplifies to:

\(Z = \dfrac{R Z_L}{R + Z_L} = \dfrac{j R \omega L}{R + j\omega L} = \dfrac{1}{\dfrac{1}{R} - j\dfrac{1}{\omega L}}\)

The magnitude (modulus) and phase angle of the impedance are:

Modulus: \(|Z| = \dfrac{1}{\sqrt{\dfrac{1}{R^2} + \dfrac{1}{\omega^2 L^2}}}\) in ohms (Ω)

Phase angle: \(\theta = \arctan\left(\dfrac{R}{\omega L}\right)\) in radians or degrees