Problem 1:

Figure 1(a)

Figure 1(b)

It is often convenient in the analysis of AC circuits to convert the series R-C or R-L branch to an equivalent parallel branch and vice versa as shown in Fig. 1 (a) and (b).

Given that the operating frequency is ω (rad/s);

a) Find the values of RP and CP shown in Fig. (a) in terms of RS, CS and ω

b) Find the values of RS and CS shown in Fig. 1(a) in terms of RP, CP and ω

c) Find the values of RP and LP shown in Fig. 1(b) in terms of RS, LS and ω

d) Find the values of RS and LS shown in Fig. 1(b) in terms of RP, LP and ω

Problem 2:

In the circuit shown in Fig. 2:

a) Find the voltage VAB (magnitude and angle)

b) Plot the magnitude of VAB (y-axis) against XL (x-axis)

c) Calculate the active power dissipated in each resistance

d) Calculate the reactive power dissipated in XL

e) Calculate the total current I

f) Calculate the power factor of the circuit

g) Calculate the total apparent power delivered by the voltage source

h) Prove that the total generated apparent power is equal to the total dissipated apparent