Calculating the current in a network of impedance elements

[Chickwolf]

Greeting all, working through the revision notes and am being stumped by a question I was hoping someone may be able to help me with. The question and all the workings for it are attached, but I cant seem to understand what the sums labelled two and three actually are. I get that sum 1 is showing the expression for the voltage, but for the life of me I cant understand 2 and 3. Its probably something silly but was hoping someone could help. Cheers!

 

[dorke]

That is easy actually:

You have 3 KVL loop equations : (1)-green, (2)-blue,(3)-purple
In each loop equation .
the left-hand side is the value of the "voltage source" in the loop
and the right-hand side is the sum of the voltages on each component expressed in the form of
Vzi=Zi * Izi
(voltage on element Zi) =(impedance of element Zi) * (current through the element Zi)
The current through an element is the sum of the currents (i1 ,i2,i3) through it (with direction taken into account).

 

[Chickwolf]

Fantastic thank you! Really cleared that up for me, knew it would be something simple I just wasn't picking up on. Cheers!