Let us now define resonance. In a two-terminal electrical network containing at least one inductor and one capacitor, resonance is the condition which exists when the input impedance of the network is purely resistive

sinusoidal voltage: V =V29 A sinusoidal current: I= We define the complex powerS=vi=V∠9,I∠-9 =V∠,-=V∠=+ jVI sin=P+j P=VIcos 9 --active(average) power

Example 1: If 0=4v2 cos\tV, Z=2/600Q2 Find p(t)and P. Solution:

The phasor diagram is a name given to a sketch in the complex plane of the phasor voltages and currents throughout a specific circuit

8-1 Nodal, mesh and loop analysis Nodal analysis:

《电路》（英文版）7-6 Phasor relationships for、and R:

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 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

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

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)