Physics Lesson 15.5.3 - Kirchhoff's Voltage Law

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Welcome to our Physics lesson on Kirchhoff's Voltage Law, this is the third lesson of our suite of physics lessons covering the topic of Kirchhoff Laws, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Kirchhoff's Voltage Law

The discussion above regarding currents behaviour is not sufficient to find the missing quantities in a circuit. We must also know what happens to the potential differences (voltages) in each component and how they are related to the electromotive forces produced by the sources. This information can be obtained using the Kirchhoff's Second Law (Kirchhoff's Voltage Law). It is a formulation of the law of conservation of energy in a closed path (loop) adapted for voltages. The Kirchhoff's Second (Voltage) Law states that

The algebraic sum of all the voltages around any closed loop in a circuit is equal to zero.

This law is true because a circuit loop is a closed conducting path and therefore, no energy is lost. The charge flowing through a closed loop is also constant. Recall the relationship between electric potential energy and potential difference

W = Q ∙ ∆V

The mathematical form of the Kirchhoff's Voltage Law is

∑emf = ∑∆V

Ohm's Law is just a special case of Kirchhoff's Law of Voltages because in a single resistor and single source circuit (if not considering the resistances of wire and source) we have

emf = I ∙ R = ∆V

The Kirchhoff Law of Voltages is particularly useful when there is more than source in a single branch, especially when they are connected in opposite directions as shown in the first figure of this paragraph. Let's illustrate it with numbers to understand this point.

Example 4

What is the current flowing in the circuit below? Do not consider the resistance of wire and that of battery.

Physics Tutorials: This image provides visual information for the physics tutorial Kirchhoff Laws

Solution 4

The first thing to do is to determine the direction of current flow as the two sources produce currents in opposite directions. Given that the first battery produces a higher current, we choose the clockwise direction (the direction determined by the first battery) as the direction of current flow. Hence, we must assume the emf of the 12 V battery as negative, as it produces an anticlockwise current. Thus, we obtain

emf₁-emf₂=I ∙ R

Therefore, we obtain for the current flowing in the circuit

I = emf₁ - emf₂/R
= 18 V - 12 V/3 Ω
= 2 Ω

You have reached the end of Physics lesson 15.5.3 Kirchhoff's Voltage Law. There are 4 lessons in this physics tutorial covering Kirchhoff Laws, you can access all the lessons from this tutorial below.

More Kirchhoff Laws Lessons and Learning Resources

Electrodynamics Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
15.5	Kirchhoff Laws
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
15.5.1	Junctions, Nodes, Paths, Branches and Loops
15.5.2	Kirchhoff's Current Law
15.5.3	Kirchhoff's Voltage Law
15.5.4	Solving Complex Circuits using the Kirchhoff Laws

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