Question

What is Kirchhoff's Voltage Law?

Answer 1

Kirchhoff's Voltage Law (KVL) is one of the fundamental principles in electrical circuits. It states that the sum of all electrical voltages around any closed loop or circuit is always zero. In simpler terms, the total amount of electrical energy supplied by sources (like batteries) is equal to the total amount of energy used up by resistors and other components within that loop.

Mathematically, KVL is expressed as:

\[
\sum V = 0
\]

Where:

1. \( \sum V \) means the sum of all voltages in the loop.
   

1. The voltages can be either positive (for voltage rises like in batteries) or negative (for voltage drops like in resistors or other components).
   

Why does KVL work?

This law is based on the principle of energy conservation. As electrical energy moves through a circuit, it is "used up" or "converted" into other forms (like heat in a resistor). At the end of the loop, the total energy gained and lost must balance out to zero, because no energy is lost or created in an ideal circuit.

Example:

Consider a simple series circuit with a 9V battery and two resistors, one of 4 ohms and the other of 5 ohms. If you apply KVL:

1. The voltage rise across the battery is +9V.
   

1. The voltage drop across the resistors adds up to 9V (assuming current is 1A, using Ohm’s law: \(V = IR\)).
   

Thus, \( 9V - 9V = 0 \), which satisfies KVL.

In summary, KVL helps us understand how voltage behaves in a circuit and is essential for analyzing and solving circuits, particularly when dealing with multiple components.