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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 Circuits Equations 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) Equations (cont’d) Determination of time constant 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