Equivalent circuit of voltage regulator

Question

Assignment:

Question 1. Figure represents the equivalent circuit of a voltage regulator where an unregulated 12V source is used to provide a stabilised voltage Vout using an 8V zener diode.

Using Kirchhoff’s voltage law and by writing the appropriate equations find:

i. The currents  i₂ & i₃.   
ii. The output voltage Vout.   
iii. The power dissipated by the zener diode (resistor RZ).

Question 2. A p.d. of   V  is connected between terminals A and B of  the network below For a frequency of 32.274861 kHz calculate :

a. The j notation impedance of the network.   
b. The polar representation of the impedance in the form R ∠Θ giving the answer as a positive angle.
c.  The magnitude of the voltage across C₂ and its phase relative to the supply voltage.