What is Kirchhoff’s Voltage Law (KVL)? Explain with an example.

Simple Answer:

Kirchhoff’s Voltage Law (KVL) states that the sum of all voltages in a closed electrical loop is always equal to zero. This means that the total voltage supplied in a circuit is completely used up by the components, such as resistors, capacitors, or other loads. KVL is based on the law of conservation of energy, which ensures that no energy is lost or created in an ideal circuit.

For example, if a battery of 10V powers a circuit with two resistors that drop 6V and 4V, then:

10V−(6V+4V)=010V – (6V + 4V) = 010V−(6V+4V)=0

Detailed Explanation:

Kirchhoff’s Voltage Law (KVL) is one of the fundamental laws in electrical engineering. It is also called Kirchhoff’s Second Law and is used to analyze circuits with multiple components.

Understanding Kirchhoff’s Voltage Law (KVL):

  • A closed loop is a complete electrical path in a circuit.
  • KVL states that the sum of all voltages in any closed loop is equal to zero.
  • This means that the voltage gained from the power source is completely used up by the circuit components.
  • Mathematically, KVL is written as:

∑V=0\sum V = 0∑V=0

where:

  • ∑V\sum V∑V is the algebraic sum of voltages in the loop.
  • Voltage sources (like batteries) are taken as positive, and voltage drops (across resistors or loads) are taken as negative.

Example of Kirchhoff’s Voltage Law:

Consider a simple circuit with:

  1. A 12V battery as the voltage source.
  2. Two resistors R₁ (drops 7V) and R₂ (drops 5V) connected in a loop.

Applying KVL:

12V−7V−5V=012V – 7V – 5V = 012V−7V−5V=0

This confirms that the total voltage supplied is completely used by the resistors.

Applications of Kirchhoff’s Voltage Law:

  1. Analyzing Complex Circuits – Helps in solving multi-loop circuits.
  2. Finding Unknown Voltages – Used to calculate voltage drops across circuit elements.
  3. Verifying Circuit Design – Ensures the circuit follows energy conservation principles.
  4. Power Distribution Systems – Helps in designing stable power networks.
Conclusion:

Kirchhoff’s Voltage Law is an important rule in electrical engineering. It ensures that the sum of voltages in a closed loop is always zero, meaning energy is neither created nor lost. This law is essential for designing, troubleshooting, and analyzing electrical circuits.