Circuit RL

A circuit RL is a Electrical circuit containing a resistance and a winds in series. It is said that the reel is opposed transitorily to the establishment of the current in the circuit.

The differential equation which governs the circuit is the following one:

U = L \ frac {di} {dt} +R_t.i

With:

$U$ the tension at the boundaries of the assembly, in V;
$i$ the intensity of the electric current in has;
$L$ the Inductance of the reel in H;
$R_t$ the total resistance of the circuit in Ω.

Transitory mode

The general solution, associated with the initial Condition

i_ {winds} (t=0) = 0

, is:

i_ {winds} = \ frac {E} {R_t} (1 - e^ {- \ frac {T} {\ tau}})

\ tau = \ frac {L} {R_t}

With:

$i_ {winds}$ the intensity Electric current crossing the assembly, in has;
$L$ the Inductance of the reel in H;
$R_t$ the total resistance of the circuit in Ω;
$E$ the electromotive force of the generator, in V;
$t$ the Time in S;
$\ tau$ the Time-constant of the circuit, in S.

It is the time-constant $\ tau$ which characterizes the “duration” of the transitory mode. Thus, the closed-circuit current is established to 1% near at the end of a duration of 5 $\tau$ .

When the current becomes permanent, the equation is simplified in U=Ri because Ldi/dt=0 .

Permanent sinusoidal mode

In sinusoidal Mode permanent, the circuit can be characterized by a complex impedance Z being worth

Z = R_t+j \ Omega L

See too

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