Fluid flow analogy

Power and energy in an inductor

Capacitor v-i equation

Capacitor Power equation

Capacitor : power and energy

Capacitor : power and energy

The self- and mutually induced voltages

The self- and mutually induced voltages

7-1 . The natural response of an RL circuit

• Independent current source IS .

• The switch has been closed for a “long time”.• L di/dt = 0 at t <0 (before the release of stored energy) ;

the inductor appears a s a short circuit .

• No current in R0 and R ; all the current appears in L branch .Finding v(t) and i(t) for t>=0 .

Expressions for the current

LR CircuitsEquations

RL circuits (cont’d)

RL circuits (cont’d)

RL circuits (cont’d)

Time constant

Time constant(1% of the initial value at five time constants)

-less than 5 constants : the transient response- exceeds 5 constants : steady- state response

Time constant (cont’d)

Determination of time constant

Equations (cont’d)

Calculating the response of RL circuit

7-2 The natural response of an RC circuit

• An RC circuit is analogous to an RL circuit• The switch has been in the position for a long time such

that all the elements in the circuit reach a steady-state condition .

• A source voltage exists between the terminals.• Circuit after switching is shown in Fig. 7-11 .

Expression for the voltage

Circuit consisting of R,

C and Vg