circuits

capacitor

q(t)/v(t)

capacitor current

C*dv(t)/dt

capacitor voltage

capacitor power

v*i

v*c*dv/dt

capacitor energy

capacitor in parallel

add

capacitor in series

1/ceq = 1/c1 + 1/c2

inductor voltage

v(t) = L* di/dt

inductor current

inductor power

inductor energy

inductor in parallel

like resistors in parallel

inductor in series

add

RC circuit - discharging

RC circuit - charging

general solution for rc/rl circuits

time constant for capacitor

tao = RC

RL voltage

RL circuit current

RL time constant

tao = L/R

steady state capacitor

becomes open circuit

steady state inductor

becomes short circuit

steady state initial conditions

no effect on ss behaviour

sinusoidal voltage

phase angle

tells use delay between v(t) and Vmcost(wt)

finding phase from graph

sin(z) sinusoidal manipulation

cos(z-90)

-cos(z) sinusoidal manipulation

cos(z+-180)

time domain

frequency domain

impedance (ohms)

Z=V/I

capacitor phasor relationship

current leads voltage by 90deg

inductor phasor relationship

voltage leads current by 90deg

impedance in series

add

impedance in parallel

resistor in parallel

capacitor in ss DC

open circuit

inductor in ss DC

short circuit

Vrms

Irms

average power, Vrms

average power, Irms

power for resistive load

power for inductive load

power for capacitive load

power for a general load

average power = real power = true power

Watts

apparent power

VA

reactive power

VAR

power factor

phase difference bw voltage + current

relationship bw average/apparent/reactive

max power transfer for resistive circuits

max average power transfer for resistive + reactive circuits

max power transfer current thev

max power transfer power delivered

maximum power in thev

current division

voltage division

feedback systems - in series

H1(s)H2(s)

feedback systems - in parallel

H1(s) + H2(s)

pole stability - H(s)

eigenvalues negative, in LHP, ≠0

pole stability - H(z)

inside unit circle, less than 1, ≠1