Consider the circuit shown below in which a generator with complex impedance Zg
ID: 1924685 • Letter: C
Question
Consider the circuit shown below in which a generator with complex impedance Zg = Rg +jXg is connected to a complex load, ZL = RL + jXL. V0 is the rms voltage amplitude ofthe sinusoidal signal source.
(a) Determine the optimum load impedance (that is, its real and imaginary parts) in termsof the generator resistance, Rg, and generator reactance, Xg, that results in the generatordelivering its maximum (average) power to the load.
(b) Under these conditions, what average power (in terms of Vg, Rg, and Xg) is deliveredto the load? (Note: the maximum average power a generator is capable of delivering iscalled the generator’s available power.)
Explanation / Answer
a)Generator delivers maximum power when the load impedence is equal to the source impedence.. ie,RL+jXL=Rg+jXg on comparing real and imaginary parts we get RL=Rg and XL=Xg b)the maximum power delivered to the load is given in the following way.. The total current in the circuit when RL=Rg and XL=Xg is given by i=Vo/(2Rg+j2Xg)=Vo/2(Rg+jXg) the maximum power delivered to the load is given by P=i^2(RL+jXL) but RL=Rg and XL=Xg =>P=[Vo/2(Rg+jXg)]^2{Rg+jXg} =>P=Vo^2/4(Rg+jXg)