AC Network?

Question

In the following AC network, the speaker is modelled as a 5-Ohm resistor.

a. Find the average power delivered to the speaker.

b. Without removing current circuit components and using one additional ideal transformer and one additional capacitor, please propose and present a simple circuit modification to ensure maximum power delivered to the speaker. Determine that maximum power.

Answer 1

Z = 15+j20 = 25 /53.1°

Vrms = 220

Irms = 220/(15+j20) = 8.8 /53.1°

I²R = 8.8²*5 =387W <<<<< a.

Capacitor in series with the speaker Xc = -10

Transformer with turns ratio Vp/Vs = √2

The impedance seen by the source =10+j20 +[√2)²(5-j10)] = 20+j0

Irms = 220/20 = 11A

11²*10 = 1210W <<<<< b.