New Way To Use Kirchhoff's Current Law Simplifies Circuit Analysis

May 22, 2008
How to get the simplerst equations using Kirchhoff's fundamental current and voltage laws forcircuit analysis.

The well-known Kirchhoff’s current law is often used in linear circuit analysis. It’s also called Kirchhoff ’s first law, Kirchhoff ’s point rule, Kirchhoff ’s junction rule, and Kirchhoff ’s first rule. The law says that at any point in an electric circuit, the sum of currents flowing toward the point is equal to the sum of currents flowing away from the point. That is, the net current flow into the point is always zero.

This article describes a new way of using Kirchhoff’s current law to make circuit analysis clearer and simpler. For example, using the very simple example circuit in Figure 1, the current law says:

We can write the above equation as:

and rearrange it to:

Equation 3 is equivalent to Equation 1, but it could have different meanings. The left side of Equation 3 means currents flowing away from the point through resistors as if V1 and V2 are grounded. The right side means all currents flowing into the point as if the middle point is grounded. It’s much easier to write equations in this way. Another example involves equations for a differential amplifier (Fig. 2). Using the new method, we have:

Solving the above equations:

Extending this technique to a more complicated circuit (Fig. 3) leads to four equations for the four nodes:

Thus, the new technique for using Kirchoff ’s law generates equations that are simple and easy to use.

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