Kirchhoff's 2nd Law

A notable voltage drop takes place when the current travels through a component such as a resistor.

Kirchhoff’s 2nd Law states that the sum of all voltages around a closed loop in any circuit must be equal to zero.

Kirchhoff’s 2nd Law is also called Kirchhoff’s Voltage Law, or the Law of Conservation of Voltage.

**Kirchhoff’s 2nd Law allows us to understand voltage and its usage across complex circuits with multiple components and paths.**

At its most basic level, Kirchhoff’s 2nd Law tells us that the total voltage supplied to a closed-loop circuit must be appropriately divided, and used, by all the resistors in that loop.

Or, if we look at from the other direction, we can say that the at the end of the loop the total voltage available must be equal to zero.

With each resistor, the voltage supplied at the start of the circuit experiences a voltage drop. Meaning that the voltage entering the resistor is less than what comes out the other side.

How much of the supplied voltage each resistor consumes, or drops the total by, is determined by looking at a combination of the amperes of the circuit current, and the ohms values of the resistors. This is particularly useful when dealing with series circuits and voltage divider circuits in electrical engineering.

Practice Questions

Test your new knowledge on Kirchhoff's second law by answering these questions.

Test it out

Tap the diagram for more information and click on the buttons to change a component and see what happens!

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Example calculations

In order to work with Kirchhoff's 2nd Law, electrical engineers need to understand and work with a variety of calculations. Here are just a few:

In a single loop the sum of all voltages around a closed loop in any circuit must be equal to zero:

$\Sigma V = 0$

$V_1 + V_2 + V_3 = 0$

$V_{AB} + V_{BC} + V_{CD} = 0$

Volt Supply:

$V_s = I(R_1 + R_2 + R_3)$

$V_s = I \Sigma R$

Circuit Current:

$I = \frac{V_S}{R_T} = \frac{V_S}{R_1 + R_2 + R_3}$

Current | $I$ |

Voltage | $V$ |

Voltage Supplied | $V_s$ |

Resistor | $R$ |

Amperes | $A$ |

Ohms | $\Omega$ |

**Kirchhoff’s 2nd Law allows us to understand voltage and its usage across complex circuits with multiple components and paths.**

At its most basic level, Kirchhoff’s 2nd Law tells us that the total voltage supplied to a closed-loop circuit must be appropriately divided, and used, by all the resistors in that loop.

Or, if we look at from the other direction, we can say that the at the end of the loop the total voltage available must be equal to zero.

With each resistor, the voltage supplied at the start of the circuit experiences a voltage drop. Meaning that the voltage entering the resistor is less than what comes out the other side.

How much of the supplied voltage each resistor consumes, or drops the total by, is determined by looking at a combination of the amperes of the circuit current, and the ohms values of the resistors. This is particularly useful when dealing with series circuits and voltage divider circuits in electrical engineering.

Practice Questions

Test your new knowledge on Kirchhoff's second law by answering these questions.