2.1: Basic Laws

NETWORK TERMINOLOGY

1. Branches: single elements and its terminals.
2. Nodes: Points of connection between one or more branches/elements
3. Loop: Closed path in which each element is visited once.
4. Mesh: Loop without any other loops inside it.

OHM'S LAW

Voltage V across the resistor is directly proportional to the current going through it.

V = IR

[Volts] = [Amps][Ohms]

• CASE I: Short circuit

If resistance = 0, voltage = 0

• CASE II: Open circuit

If resistance = infinitive, current = 0

KIRCHOFF'S LAWS

1. Kirchoff's current law (KCL): The alebraic sum of currents entering a node (or closed boundary) is zero.

Example:
In the circuit below, determine I1 and I2

By adding the current at each node we have:

I1 = 8mA + 4mA = 12mA

I2 = 8mA - 2mA = 6mA

2. Kirchoff's voltage law (KVL): The algebraic sum of all voltages around a closed loop is zero.

Example:
In the circuit below, determine Vbd

Adding all the voltage components that go from B to D, we have:
Vbd = 6V + 2V = 8V

EQUIVALENT RESISTANCE

• SERIES: 

a) Any number of resistors in series is equivalent to the sum of all resistors.

b) Series elements are elements through which the same current flows.

c) Voltage divider in series resistors is given by:

VR1 = Vs x (R1/(R1+R2)

• PARALLEL: 

a) Any number of resistances in parallel is equivalent to the product of all resistances divided by the sum of all resistances.

b) Elements share the same voltage at the same two nodes.

c) Current divider is given by:

IR1 = Is x (1/R1 / (1/R1 + 1/R2)