Define and explain Kirchhoff's Voltage or Loop Rule. Provide three (3) examples of its use

Kirchhoff's Voltage Law, also known as Kirchhoff's Loop Rule, is a fundamental principle in electrical engineering and physics that deals with the conservation of energy around a closed loop or circuit. It states that the sum of the electromotive forces (emfs) in any closed loop or mesh in a network is always equal to the sum of the potential drops in that loop. In simpler terms, the total voltage supplied in a closed circuit loop is equal to the total voltage drop across the circuit.

This law is based on the conservation of energy, which states that energy cannot be created or destroyed, only transferred. In the context of an electrical circuit, this means that the energy supplied by the power source (such as a battery) must be equal to the energy used by the resistors (or other components) in the circuit.

Here are three examples of its use:

1. Simple DC Circuit: Consider a simple DC circuit with a battery of 9V and a resistor of 3 ohms. According to Kirchhoff's Voltage Law, the voltage supplied by the battery (9V) is equal to the voltage drop across the resistor. This can be used to calculate the current flowing through the circuit using Ohm's Law (V=IR), which would be 3A in this case.

2. Series Circuit: In a series circuit with a 12V power source and two resistors of 3 ohms and 4 ohms, the total voltage drop across the resistors must equal the voltage supplied. This means the voltage drop across the 3 ohm resistor plus the voltage drop across the 4 ohm resistor equals 12V. This can be used to calculate the current in the circuit and the individual voltage drops.

3. Parallel Circuit: In a parallel circuit with a 9V power source and two resistors of 3 ohms and 6 ohms, Kirchhoff's Voltage Law can be used to show that the voltage drop across each parallel branch is equal to the voltage of the power source. This means the voltage drop across the 3 ohm resistor is 9V and the voltage drop across the 6 ohm resistor is also 9V. This can be used to calculate the current through each branch.