circuit rl

Procedures to get natural response of RL RC circuits 1 Find the equivalent circuit 2 Find the initial conditions: initial current I 0 through the equivalent inductor or initial voltage V 0 across the equivalent capacitor 3 Find the time constant of the circuit by the values of the equivalent R L C: 4 Directly write down the

Chapter 8 Basic RL and RC Circuits Fig 8 1 Fig 8 6 A series RL circuit for which i(t) is to be determined A plot of the exponential response versus time Fig 8 11 AA parallel RC circuit for which v(t) is to be determined Fig 8 21 (a) A voltage-step function is shown as the source Fig 8 19

Specifications: E R (emf) (resistance) L (inductance) Switch S: a: current buildup b: current shutdown Time-dependent quantities: I(t): dI dt ε b instantaneous current through inductor : rate of change of instantaneous current VR(t) = I(t)R: dI VL(t) = L dt I(t) R L instantaneous voltage across resistor : instantaneous voltage across inductor dI

The solution to this can be found by substitution or direct integration This is known as the complementary solution or the natural response of the circuit in the absence of any active sources: xc(t) = Ke t= (7) Clearly the natural response of a circuit is to decay to 0

• This chapter considers RL and RC circuits • Applying the Kirshoff’s law to RC and RL circuits produces differential equations • The differential equations resulting from analyzing the RC and RL circuits are of the first order • Hence the circuits are known as first-order circuits • Two ways to excite the first-order circuit: