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zenterix

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- TL;DR Summary
- The book I am reading, "Foundations of Analog and Digital Electronic Circuits" by Agarwal has a section on the node method of circuit analysis that says that the KCL equations used in this method contain within them all the information from all the independent KVL equations. I can't seem to see this use of the KVL equations, however.

Consider the following electric circuit in which we have node voltages labeled

I have a question about the reasoning present in the book I am reading about the node method of circuit analysis.

If we write KVL equations around the loops we get

$$-V+(V-e)+e=0$$

$$-e+e=0$$

Then

I don't understand in what way the independent statements of KVL are used when writing out a KCL equation in the node method.

As far as I can see, we are using KCL and then subbing in the expressions for the currents, which come from the element laws.

Where exactly is KVL?

I have a question about the reasoning present in the book I am reading about the node method of circuit analysis.

If we write KVL equations around the loops we get

$$-V+(V-e)+e=0$$

$$-e+e=0$$

...this choice of voltage variables automatically satisfies KVL. So to solve the circuit it is not necessary to write KVL. Instead, we will directly proceed with writing KCL equations. Furthermore, to save timethe KCL equations can be written directly in terms of the node voltages and the resistors' values.Since we have only one unknown,e,we need only one equation. Hence, at node 2,

$$\frac{e-V}{R_1}+\frac{e}{R_2}-I=0\tag{3.5}$$

Notice that the preceding step is actually two substeps bundled into one: (1) writing KCL in terms of currents and (2) substituting immediately node voltages and element parameters for the currents by using KVL and element laws.

Then

Note that in one step we have one unknown and one equation, whereas by the KVL and KCL method of Chapter 2 we would have written eight equations in eight unknowns.Further, note that both the device law for every resistor and all independent statements of KVL for the circuit have been used in writing Equation 3.5.

I don't understand in what way the independent statements of KVL are used when writing out a KCL equation in the node method.

As far as I can see, we are using KCL and then subbing in the expressions for the currents, which come from the element laws.

Where exactly is KVL?