Electricity/Electric circuit/RL circuit

RL circuit

RL series

$v_{L}+v_{R}=0$

$L{\frac {d}{dt}}i+iR=0$

${\frac {d}{dt}}i=-{\frac {1}{T}}i$

$i=Ae^{-{\frac {t}{T}}}$

$T={\frac {L}{R}}$

2 port LR

${\frac {v_{o}}{v_{i}}}={\frac {R}{R+j\omega L}}={\frac {1}{1+j\omega T}}$

$T={\frac {L}{R}}$

$\omega _{o}={\frac {1}{T}}$

$\omega =0$ . $v_{o}=v_{i}$

$\omega _{o}=\omega _{o}$ . $v_{o}={\frac {v_{i}}{2}}$

$\omega _{o}=00$ . $v_{o}=0$

2 port RL

${\frac {v_{o}}{v_{i}}}={\frac {j\omega L}{R+j\omega L}}={\frac {j\omega T}{R+j\omega T}}$

$T={\frac {L}{R}}$

$\omega _{o}={\frac {1}{T}}$

$\omega =0$ . $v_{o}=0$

$\omega _{o}=\omega _{o}$ . $v_{o}={\frac {v_{i}}{2}}$

$\omega _{o}=00$ . $v_{o}=v_{i}$