Practical Electronics/Series RL

A circuit of two components R and L connected in series
 * [[Image:RL_Series_Open-Closed.svg|100px]]

Natural Response of the cicuit can be obtained by setting the differential equation of the circuit to zero
 * $$v_L+v_R=0$$
 * $$L \frac{dI}{dt}+IR=0$$
 * $$\frac{dI}{dt}= - \frac{1}{T} I$$
 * $$\int \frac{dI}{I}= - \frac{1}{T} \int dt$$
 * $$Ln I = - \frac{1}{T} + C$$
 * $$I = e^{(- \frac{1}{T} + C)}$$
 * $$I = Ae^{- \frac{t}{T}}$$
 * $$T=\frac{L}{R}$$
 * $$e^{C}=IR$$