#### Kirchoff's Voltage Law (KVL):

The algebraic sum of the voltages around any closed path is zero. If you start from any point at one potential and come back to the same point and potential, the differenee of potential must be zero.

**Algebraic Signs:**

In detennining the algebraic signs for voltage terms in KVL equations, first mark the polarity of each voltage. A convenient system then is to consider the closed path and consider that voltage whose neggative tarminal is reached firsst as a negative term. Similarly any voltage whose positive terminal is reacched first consider it as a posittive term. This method applies to IR Voltage drops and Voltage source. The direction can be clockwise or counter clockwise.

Remember that electrons flowing into a resistor make that end negative with respect to the other end. For a voltage source, the direction of electrons returning to the positive terminal is the normal direction for electron flow, which means the source, should be a positive term in the voltage equations.

When you go around the closed path and come back to the starting point, the algebraie surn of all the voltage terms must be zero. There cannot be a potential difference for one point. If you do not come back to the start, then the algebraic sum is the voltage between the start and finish point.

You ean follow any closed path. The reason is that the voltage between any two points in a circuit is the same regardless of the path used in determining the potential difference.

**Loop equations:**

Any closed path is called loop, starting from point "A' at the top, through CEFDB, and

back to A, includes the voltage drops V1, V4, Vs and V2 and the Source Vr

The inside loop ACDBA includes V1, V3, V2 and V T' The other inside loop, CEFDC with V4, Vs and V3 does not include the voltage source.

Consider the voltage equation for the inside loop with Vr In clockwise direction, starting from point A, the algebraic sum of the voltage is

Voltage V1, V3 and V2 have the negative sign, because for each of these voltages the negative terminal is reached first. However, the source VT is a positive term because its plus terminal is reached first, going in the same direction.

For the opposite direction, going counter clockwise in the same loop from point B, V2, V3 and Vı have positive values and VT is negative, then

V2+V3+V1-VT = 0