Kirchoff’s Current Law Kirchoff’s Voltage Law Dr. A. Vennie Filippas EGRE 101 Notes

Current as Flow Electrical current represents flow of electrons Specifically, #of electrons per unit area per second

Conservation of electric charge Think of water flowing from a large pipe into two smaller pipes: At any given time, the amount of water flowing into the junction from one pipe has to equal the total amount of water flowing into each of the smaller pipes

Electric Current Electric current in a wire is flow of free electrons. If the current needs to branch out from one wire into two, the total current in the two wires has to equal the current in the one wire. I1 I2 I1=I2+I3 I3

Kirchoff’s Current Law The sum of the currents flowing into a node is equal to zero. Add the currents flowing into a node, subtract the currents flowing out of a node

Nodes – Central or connecting points

Branch – Single element or device

Branch – Single element or device I1-I2-I3=0 I1

Voltage as position If you climb up a mountain path, how far down would you have to go to get back to ground? Easy answer - add the paths going up, and subtract the paths going down. The total sum should be zero. h3 h2 h4 h1 h5

The same equation holds true, no matter how the heights are arranged More examples The same equation holds true, no matter how the heights are arranged h3 h4 h2 h5 h1

In a circuit … 12V 9V Voltage drop at R1 6V Voltage drop at R2 -3V 3V Nominal 0 Each component in a circuit will represent a voltage “rise” or a voltage “fall”

Kirchoff’s Voltage Law Try to conceptualize a path around a closed loop (see path described as “loop 1”) Subtract all voltage drops along the path - add voltage rises. The total sum is equal to zero. + Vsource - +V1- +V2- +V3- +V4-

Usage Kirchoff’s current law and voltage law are used to calculate all the voltage drops and currents in a circuit. The trick is in knowing what sort of a current-voltage relationship exists for each component.

Some more voltage concepts Node Voltages: Voltage represents a difference between two points A and B. VAB is the voltage drop from point A to point B. Can use a reference point, henceforth referred to as ground. This represents a reference zero point for the voltage. VA is the voltage drop from point A to ground. VB is the voltage drop from point B to ground. VAB=VA-VB A B G VA VB VAB Using node voltages can sometimes simplify your circuit analysis

Conclusion We can use Kirchoff’s Current Law (KCL) and Kirchoff’s Voltage Law (KVL) to set up the appropriate equations to help us calculate all the currents and voltage drops in a circuit. We will also need to apply other relationships, specifically those that characterize the components in the circuit. One example of such a relationship is Ohm’s Law, that defines the voltage drop across a resistor when one knows the current going through it. (V=IxR)