KIRCHHOFF'S LAWS AND ELECTROMAGNETISM

Kirchhoff's Laws and Electromagnetism

Kirchhoff's Current Law (KCL)

At every node, the sum of all currents entering a node must equal zero (Trajkovic 2005). What this law means physically is that charge cannot accumulate in a node; what goes in must come out.KCL states that the algebraic sum of the currents in all the branches which converge in a common node is equal to zero

SIin = SIout

Kirchhoff's Voltage Law

Kirchhoff's Voltage regulation states that the algebraic sum of the voltages between successive nodes in a close route in the network equals to  zero.

SE = SIR

Steps to solve circuit by Kirchhoff's Law

1. Construct circuit with circuit magic schematics editor.

2. Construct loops. Number of loops (and number of Kirchhoff's Voltage laws equations) can be determined using following formula. Loop cannot include branches with current sources. The current sources resistance equal infinity.

Loop Number = branchNumber - (Nodes Number -1) - current sources Number

3. Select Analyze->Solve by Kirchhoff's laws menu item

4. in dialog  box press OK button. If no warning shown.

5. Read solution.

Kirchhoff's Current Law (KCL)

Let's take another detailed look at that last parallel example circuit:

Solving for all values of voltage and current in the circuit:

At this point, we know the value of each branch current and of the total current in the circuit (Nilsson2007). We understand that the total current in an aligned circuit that must equate the sum of the branch currents, but there's more going on in this circuit than just that. Taking a gaze at the currents at each cable junction point(node) in the circuit, we should be able to have a look at something else:

At each node on the negative "rail" (wire 8-7-6-5) we have current splitting off the major flow to the next branch resistor. At each node on the positive"rail" (wire 1-2-3-4) we have current joiningtogether to form the major flow from each of the next branch resistor. This detail should be fairly obvious if you take the water pipe circuit analogy with every branch node acting as a "tee" fitting, the water flow splitting or merging with the major piping as it journeys from the output of the water pumpin the direction of the returnreservoir or sump.

If we were to take a closer look at one specific "tee" node, such as node 3, we look that the current entering the node is equal in magnitude to the present exiting the node:

From the right and from the base, we have two currents going into the cable attachment labeled as node3. To the left, we have a  single current exiting the node identical in magnitude to the sum of the two currents entering. To refer to the plumbing analogy: so long as there are no leaks in the piping, what flow goes into the fitting should furthermore exit the fitting. This is the same for any node ("fitting"), no issue how many flows are going into or exiting. Mathematically, we can articulate this general relationship as such: ...