# Nillsons Electrical Circuits Confusion

I'm reading this book Nilssons electrical circuits and I'm beginning to get frustrated/confused on some of the circuit diagrams. For instance this simple circuit with resistors in series. I understand that with Kirchoffs laws the sum of two currents at a node = 0 fair. But what I don't understand is why the drawings are drawn how they are (see below)

How is it possible with these resistors in series that current could travel seemingly randomly in opposite directions. R1 moves forward then R2 moves backwards then forward again. It's just really confusing me because I don't see how the current in a series of resistors can flip flop directions. ## 1 Answer

Kirchoff's current law (KCL) says the algebraic sum of the currents into a node is zero. Since current is the delivery of charge per unit time the law is based on conservation of charge. If the algebraic sum were greater than zero, charge would be accumulating at the node. If negative, charge would be depleting at the node. KCL is usually applied to nodes involving 3 or more branches. You are free to assume any directions of current that you please, because if the analysis is done properly, it will tell you what the actual directions are.

The diagram above is a trivial application of the law. It is obvious that all the currents are clockwise given the polarity of the voltage source and only one loop. But it comes out that way if you apply the law to each node.

Nodes $$b$$ and $$g$$ violate the law unless one current of each pair is in the opposite direction. Nodes $$a$$, $$d$$, and $$f$$ do not violate the law; however the law does not say which direction the current flows. The currents at $$f$$ flow in the opposite direction to those in $$a$$ and $$d$$. However, we know that the direction for the current $$I_{S}$$ is correct because, by convention, current flows out of the positive terminal of the voltage source and there is only one voltage source in the circuit. Consequently, the actual direction of the currents at node f is opposite those shown. Then the direction of all currents will be the same.

Like I said, it is a trivial exercise in the case of this circuit, but not when nodes have multiple branches.

The same applies to Kirchoff's Voltage Law (KVL) or loop analysis. The directions of loop currents can be assumed arbitrarily, but the analysis will give the proper directions.

Hope this helps.