# RL CIRCUIT

Cuthbert Nyack

The RL circuit is shown schematically above.

The Impedance of the circuit is
Z = (R + jwL)

The magnitude of the impedance of the circuit is given by:-

|Z| = Ö(R^{2} + w^{2}L^{2})

The phase of the impedance of the circuit is given by:-

Ðq = atan
(wL/R)

The phase of the current and V_{r} is
Ð-q.

V_{l} is
advanced relative to V_{r} by 90°.
q

The variation of the sinusoidal voltages V_{s}
(green curve), V_{r} (orange curve) and
V_{l} (red curve) are shown by the above
applet as a function of frequency and time constant
(T = L/R). Frequency is expressed in terms of 1/T.
Two periods are shown for all frequencies. A Bode plot is shown
in the background. The white line indicates the point on the bode plot
at which the voltages are shown.

A phasor diagram showing the variation of V_{r}
and V_{l} with frequency is shown above. The
orange line represents the voltage across the resistor,
the red line represents the voltage across the inductor,
the green line represents the source voltage and the 2
purple lines complete the parallelogram showing that the
resultant of V_{r} and V_{l} is V_{s}.
V_{l} is always leading V_{r} by 90°.
Note that at low
frequencies most of the voltage appears accross the resistor
while at higher frequencies the voltage is mostly accross the inductor.

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COPYRIGHT © 1996 Cuthbert A. Nyack.