Common Terms

Branch

A branch represents a single element, such as a resistor or a battery.

Node

A node is the point connecting more than 1 branches. Denoted by a dot.

Note

All points in a circuit that are connected directly by ideal conductors can be considered to be a single node.

Two terminal element

An element connected to two nodes. Branches are two terminal elements.

Loop

A loop is a closed path through a circuit in which no node is encountered more than once except the start/finish node.

Mesh

A mesh is a loop without having other loops inside it. Subset of loops.

Connection types

Delta connection

• Doesn’t have a neutral wire. Neutral point is imaginary.
• Delivers more power

$$V_P = V_L \;\;\; \land \;\;\; I_L = \sqrt{3} I_P$$

Star connection

$$I_P = I_L \;\;\; \land \;\;\; V_L = \sqrt{3} V_P$$

Delta-Star conversion

Delta to Star

$$R_{\text{A}} = \frac{R_\text{AB} \times R_\text{AC}}{R_\text{AB} + R_\text{BC} + R_\text{AC}}$$

$R_\text{B}, R_\text{C}$ can be found similarily. $$

Star to Delta

$$R_{\text{AB}} = \frac{(R_\text{A} \times R_\text{B}) + (R_\text{B}\times R_\text{C}) + (R_\text{C} \times R_\text{A})}{R_\text{C}}$$

$R_\text{BC}, R_\text{AC}$ can be found similarily. $$