Kirchhoff's Current Law

DC Circuits
Kirchhoff's Current Law

This fundamental law results from the conservation of charge. It applies to a junction or node in a circuit -- a point in the circuit where charge has several possible paths to travel. In Figure , we see that IA is the only current flowing into the node. However, there are three paths for current to leave the node, and these current are represented by IB, IC, and ID.  Once charge has entered into the node, it has no place to go except to leave (this is known as conservation of charge). The total charge flowing into a node must be the same as the the total charge flowing out of the node. So, IB + IC + ID = IA Bringing everything to the left side of the above equation, we get (IB + IC + ID) - IA = 0

Figure : Possible node (or junction) in a circuit

Then, the sum of all the currents is zero. This can be generalized as follows

Ohm's Law

Ohm's Law is the mathematical relationship among electric current, resistance, and voltage. The principle is named after the German scientist Georg Simon Ohm.

In direct-current (DC) circuits, Ohm's Law is simple and linear. Suppose a resistance having a value of R ohm

                                             s carries a current of I amperes. Then the voltage across the resistor is equal to the product IR. There are two corollaries. If a DC power source providing E volts is placed across a resistance of R ohms, then the current through the resistance is equal to E/R amperes. Also, in a DC circuit, if E volts appear across a component that carries I amperes, then the resistance of that component is equal to E/I ohms.

Mathematically, Ohm's Law for DC circuits can be stated as three equations:

E = IR
I = E/R
R = E/I
When making calculations, compatible units must be used. If the units are other than ohms (for resistance), amperes (for current), and volts for voltage), then unit conversions should be made before calculations are done. For example, kilohms should be converted to ohms, and microamperes should be converted to amperes