Kirchhoffs Circuit Law

Kirchhoffs Circuit Laws allow us to solve complex circuit problems by defining a set of basic network laws and theorems for the voltages and currents around a circuit

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Using Kirchhoff’s circuit laws, specifically the junction rule and the closed loop rule, one can calculate and determine the currents and voltages within any closed circuit, provided the values of the electrical components are known.

As discussed in the resistors tutorial, the equivalent resistance (R_T) can be found when multiple resistors are connected in series, parallel, or combinations of both, and these circuits adhere to Ohms Law.

In more complex circuits like bridge or T networks, Ohm’s Law alone may not be sufficient for finding voltages or currents. For such calculations, specific rules are needed to derive the circuit equations, and Kirchhoffs Circuit Laws come into play.

Gustav Kirchhoff, a German physicist, formulated these laws in 1845, providing a set of rules that address the conservation of current and energy within electrical circuits. The two fundamental laws are commonly known as Kirchhoff’s Circuit Laws. One of the laws, Kirchhoffs Current Law (KCL), deals with the current flowing within a closed circuit. The other law, Kirchhoffs Voltage Law (KVL), addresses the voltage sources present in a closed circuit.

Kirchhoffs First Law – The Current Law, (KCL)

Kirchhoffs Current Law (KCL) asserts that the total current or charge entering a junction or node is precisely equal to the charge leaving the node, as there is no other path for the charge to go except to exit. Essentially, no charge is lost within the node. In mathematical terms, the algebraic sum of all the currents entering and leaving a node must be equal to zero, expressed as I_(exiting)+I_(entering)=0. This principle, introduced by Kirchhoff, is commonly referred to as the Conservation of Charge.

Kirchhoffs Current Law

In this scenario, the three currents entering the node, namely I1, I2, and I3, are considered positive values, while the two currents leaving the node, I4 and I5, are treated as negative values. Consequently, the equation can be alternatively expressed as:

I1+I2+I3−I4−I5=0

The term “node” in an electrical circuit typically denotes a connection or junction where two or more current-carrying paths or elements, such as cables and components, meet. It is essential for a closed circuit path to exist for current to flow either into or out of a node. Kirchhoff’s current law proves useful when analyzing parallel circuits.

Kirchhoffs Second Law – The Voltage Law, (KVL)

Kirchhoff’s Voltage Law (KVL) asserts that “in any closed loop network powered by a voltage source, the total voltage around the loop equals the sum of all the voltage drops within the same loop,” and this sum is equal to zero. Simply put, the algebraic sum of all voltage sources and voltage drops within a closed loop must be zero. This is because the algebraic sum of the voltage drops is equal to the algebraic sum of the voltage sources. Kirchhoff’s Voltage Law is grounded in the principle of the Conservation of Energy.

Kirchhoffs Voltage Law

When applying Kirchhoff’s Voltage Law (KVL) in a closed loop, begin at any point in the loop and continue in the same direction, noting the direction of all voltage drops, whether positive or negative. Ensure that you return to the same starting point. Consistency in direction, either clockwise or counterclockwise, is crucial; otherwise, the final sum of voltages will not be zero. Kirchhoff’s Voltage Law is particularly useful when analyzing series circuits.

In the analysis of both DC and AC circuits using Kirchhoffs Circuit Laws, various definitions and terminologies describe the parts of the circuit under examination. These include terms like node, paths, branches, loops, and meshes. Familiarity with these terms is essential for effective circuit analysis.

Common DC Circuit Theory Terms

Circuit: A circuit is a closed loop conducting path in which electrical current flows.
Path: A path refers to a single line of connecting elements or sources within the circuit.
Node: A node is a junction, connection, or terminal within a circuit where two or more circuit elements are connected or joined, providing a connection point between branches. A node is typically indicated by a dot.
Branch: A branch is a single or a group of components, such as resistors or a source, that are connected between two nodes.
Loop: A loop is a simple closed path in a circuit where no circuit element or node is encountered more than once.
Mesh: A mesh is a single closed loop series path within a circuit that does not contain any other paths. There are no loops inside a mesh.

Note that:

Components are considered to be connected in series when the same current flows through all the components.
Components are considered to be connected in parallel when they have the same voltage applied across them.

Application of Kirchhoffs Circuit Laws

These two laws enable the currents and voltages in a circuit to be determined, i.e., the circuit is said to be “analyzed,” and the basic procedure for using Kirchhoffs Circuit Laws is as follows:

Assume all voltages and resistances are given (if not, label them V1, V2, R1, R2, etc.).
Assign a current to each branch or mesh (clockwise or anticlockwise).
Label each branch with a branch current (I1, I2, I3, etc.).
Find Kirchhoff’s first law equations for each node.
Find Kirchhoff’s second law equations for each of the independent loops of the circuit.
Use linear simultaneous equations as required to find the unknown currents.

In addition to using Kirchhoffs Circuit Law to calculate the various voltages and currents circulating around a linear circuit, we can also use loop analysis to calculate the currents in each independent loop, which helps reduce the amount of mathematics required by using just Kirchhoff’s laws. In the next tutorial about DC circuits, we will look at Mesh Current Analysis to do just that.

Read more Tutorials on DC Circuits
1.	DC Circuit Theory
2.	Ohms Law and Power
3.	Electrical Units of Measure
4.	Kirchhoffs Circuit Law
5.	Kirchhoffs Current Law
6.	Kirchhoffs Voltage Law
7.	Mesh Current Analysis