Class Activity (Week 11)

   This week node analysis, mesh analysis, and superposition analysis are use for circuits that contain 

resistors, inductors, and capacitors.

What is Vc in the below circuit?

Figure 1: Node Analysis and an Dependent-Current Source

Figure 2

Also source transformation is practiced again. 

 Thevenin and Norton equivalent circuits are a source transformation.

Figure 3: Thevenin and Norton equivalent circuits 

In order to find the Zth in a circuit, independent current sources must removed (open circuit), and 

independent voltage sources must short circuit. Then an arbitrary fixed current source or an arbitrary

fixed voltage source must connected to the points a and b.

Figure 4

Instantaneous and Average Power is discussed. 

  v(t) = V _m cos(ωt + θ _v )  ,  i(t) = I _m cos(ωt + θ _i )

Where V_m and I_m are the maximum values of v(t) and i(t), also θ_v and θ_i are the phase angles of the

voltage and current, respectively. The instantaneous power absorbed by the circuit is as below

formula.

p(t) = v(t)*i(t) , P(t) =  V _m I _m cos(ωt + θ _v ) cos(ωt + θ _i ) 

Pavg = ½ Re[VI*] = ½ V _m I _m cos(θ _v − θ _i )

According to average power, a resistor absorbs only power, while a inductor or a capacitor does not.

                                  
                                        MAXIMUM AVERAGE POWER TRANSFER


If Vth and Zth are used insted of a circuit, Maximum average power will occur under below 

conditions: 

Zth = Rth + j Xth     ,     Z_L = R _L + jX _L

Z_L = R _L + jX _L = R _Th − jX _Th = Z*_Th

The Maximum Average Power transferred is:        Pmax = |Vth|^2 / (8*Rth)