Question

What is Kirchhoff's Voltage Law?

Answer 1

Kirchhoff's Voltage Law (KVL) states that the sum of all electrical potential differences (voltages) around any closed loop or circuit is equal to zero. This is based on the principle of conservation of energy: the total energy gained in a loop must equal the total energy lost.

In mathematical terms:

\[
\sum V = 0
\]

Where \( \sum V \) represents the algebraic sum of the voltages in the loop.

This means that as you move around a closed circuit loop, the total increase in voltage (across sources) must equal the total drop in voltage (across resistors, capacitors, inductors, etc.).

Answer 2

Kirchhoff's Voltage Law (KVL) states that the sum of the electrical potential differences (voltages) around any closed circuit loop is equal to zero. This principle is based on the conservation of energy, which implies that the energy supplied by sources (like batteries) in the loop must be equal to the energy consumed by the resistive elements (like resistors) within the loop.

### Mathematically, KVL can be expressed as:

\[
\sum V = 0
\]

where \(V\) represents the voltage across each component in the loop. When applying KVL, you follow these guidelines:

1. **Choose a direction**: Typically clockwise or counterclockwise around the loop.
2. **Assign voltage polarities**: Positive for voltage rises (e.g., from batteries) and negative for voltage drops (e.g., across resistors).
3. **Sum the voltages**: Add up all the voltages in the chosen direction, and set the sum equal to zero.

### Example Application:

In a simple loop with a battery and two resistors, if the battery provides 12V, and the resistors drop 5V and 7V, KVL can be written as:

\[
12V - 5V - 7V = 0
\]

This confirms that the total voltage supplied equals the total voltage dropped, satisfying KVL.