A real, an imaginary, or a complex forcing function will produce a real, an imaginary, or complex response, respectively. Instead of applying a real forcing function to obtain the desired real response, we apply a complex forcing function whose real part is the given real forcing function; we obtain a complex response whose real part is the desired real response

The effective value of any periodic current is equal to the value of the direct current which flowing through a resistance R, delivers the same power to r as periodic current does

The forced response The steady state responseThe(t) has been switched into the circuit at some remote U.=V. cos ot time in the past, and the natural response has died-out completely. The forced response(steady state response)must satisfy the differential equation

In either case, leading or lagging, we say that sinusoids are out of phase () if phase angles equal they are said to be in phase(同相)

The complete response is written as the sum of the forced and the natural response, and the initial conditions are then determined and applied to the complete response to find the values of the constants

The over-damped response---- i()= A,+A, The critically-damped response-- i(t) =e (At+A2) The under-damped- response---it)e-(b1 cos+2 sino)

A1, A,----two arbitrary constants S S2----real numbers or conjugate complex Since the s,t and s,t must be dimensionless, S,, S2----(1/s)

The complete response of any RC circuit may also be obtained as the sum of the natural and the forced response

The complete response=the natural response+forced response

The series combination of a resistor and capacitor has a greater practical importance than does the combination of a resistor and an inductor