Relations de base
Indispensable régime continu
Tension, courant, flux, charge
`U = R*I`
`I = Q/t`
`phi = L*I`
`Q = C*I`
Générateur : `U = E - R*I`
Récépteur : `U = E + R*I`
Puissance, énergie
`P = U*I`
`P = (U^2)/R`
`P = R.I^2`
`W = P.t`
Indispensable régime variable
Tension, courant, flux, charge
`u = hat(U) sin(omegat + varphi)`
`u = R*i`
`u = L (di)/(dt)`
`i = C (du)/(dt)`
`i = (dq)/(dt) = L*i`
`phi = L*i`
`E = -(d phi)/(dt)`
`q = int_(t_i)^(t_f) i * dt`
`q = C*u`
Puissance
Instantanée : `p = u*i`
`P = U*I*cos(varphi)`
`Q = U*I*sin(varphi)`
`S = U*I`
`S = sqrt( P^2 + Q^2)`
`Q = P*tan(varphi)`
`cos(varphi) = P/S`
`sin(varphi) = Q/S`
Avec puissance déformante
`S = sqrt( P^2 + Q^2 + D^2 )`
`D = sqrt( S^2 + (P^2 + Q^2) )`
Énergie
`W = int_0^t p(t)*dt`
Inductance
`W = int_0^t L(di)/(dt)*i*dt`
`W = 1/2 LI^2`
Capacité
`W = int_0^t C(du)/(dt)*u*dt`
`W = 1/2 CU^2`
Pulsation
`omega = 2pif`
Constante de temps
`tau = R*C`
Impédance résistive
`Z_r = (U_r) / (I_r)`
=
`U_r^2 / P_r`
=
`P_r / I_r^2`
Impédance inductive
`Z_l = j omega L`
=
`L omega e^(j pi/2)`
Impédance capacitive
`Z_c = 1/(j omega C)`
=
`1/(C omega) e^(-j pi/2)`
Réactance inductive
`X_l = omega L`
=
`(U_(X_l)) / (I_(X_l))`
=
`U_(X_l)^2 / Q_l`
Réactance capacitive
`X_c = 1/(omega C)`
=
`(U_(X_c)) / (I_(X_c))`
=
`U_(X_c)^2 / Q_c`
Admittance
`Y = 1/Z`
Millman
`Vm = ( sum_(k=1)^N (E_k)/(Z_k) ) / ( sum_(k=1)^N 1/(Z_k) )`