Determine the unknown impedance Z that results in the curren

Determine the unknown impedance Z that results in the current through the 6 ohm resistor as shown. Write the needed impedance in both polar (magnitude and angle) and rectangular (R + jX) forms.

Solution

Voltage acrosss the capacitance and 6ohm resitance is

V1=(0.5+j0.5)*(6-j4)=5+j1

The voltage across Z impedance also V1, since z and 6-j4 are connected in parallel.

now write KVL on loop

10=4*I+(5+j1)

I=(10-(5+j1))/4=1.25 -j 0.25

I_z=I-I₀=1.25 -j 0.25-0.5-j0.5=0.75 - j0.75

Z=V_z/I_z =(5+j1)/(0.75 - j0.75)= 2.6667 + j4

Z= 2.6667 + j4

Z=4.81 and angle is 56.3