Electronics Handbook/Components/RL Network

Series RL
Circuit of R and L connected in series
 * RL_Series_Open-Closed.svg

Differential Equation of the circuit
At equilibrium the total voltage is zero
 * $$V_L + V_R = 0$$
 * $$L\frac{dI}{dt} + IR = 0$$
 * $$\frac{dI}{dt} = - I \frac{R}{L}$$
 * $$\int \frac{1}{I} dI = - \int \frac{L}{R} dt$$
 * ln I = $$(-\frac{L}{R}t + c)$$
 * I = $$A e^-\frac{t}{T} $$

Với
 * $$T = \frac{L}{R}$$
 * A = ec

The natural response of the circuit is Exponential Response

Circuit Impedance

 * $$Z = Z_R + Z_L $$
 * $$Z = R + j \omega L$$
 * $$Z = \frac{1}{R} (1 + j \omega T)$$
 * $$T = \frac{L}{R}$$