## KVL | Kirchhoff’s Voltage Law | Circuit Analysis | EE | CS School

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KVL – Kirchhoff’s Voltage Law refers to as Kirchhoff’s second law that also evident the conservation of energy around a closed loop circuit. It is the fundamental law of circuit analysis. KCL is the Kirchhoff’s first law of circuit analysis, which we discussed here. In this article we will discuss the basic concept of KVL. We also see that how we can simplify a circuit using kirchhoff’s Voltage law.

## KVL | Kirchhoff’s Voltage Law

In a close loop circuit we always have the voltage rise and fall around it by it components (i. e. voltage sources, resistors, capacitors etc). What Kirchhoff stated that the algebraic sum of voltage rise and fall around a closed loop circuit is equal to zero. Because the circuit is a closed loop, therefore no energy to lost here, therefore energy remain conserved. So mathematical form of kirchhoff’s voltage law is:

$$V_{rise}-V_{drop}=0\\\text{Or, }\sum V_{i} =0$$

So, Kirchhoff said that the amount of voltage given in the circuit and the algebraic sum of voltage drop by each components is equal.

A circuit illustrated in the figure right. It has a power source that supply or rise voltage to the circuit. And the circuit also has two resistors series connected. Now current i from the positive side of the  voltage source will start flowing through the circuit in a closed loop. As no current is divided, therefore same current will pass through the $R_{1},$ $R_{2}$ resistors. For i current, voltage drop by the $R_{1},$ $R_{2}$ across their terminal is, $iR_{1},$ $iR_{2}$. Therefore, according to Kirchhoff, $V_{rise}=V_{drop},$ or there algebraic sum is zero

So, $$V+(-iR_{1})+(-iR_{2})=0$$

$$\text{Or, }V=iR_{1}+iR_{2}$$

$$\text{Or, }V=i(R_{1}+R_{2})$$

So, This is the mathematical form of KVL – Kirchhoff’s Voltage law. Which provides that if current complete a closed path then the voltage drop by the current is always equal to the voltage provided in the circuit. Or, in other way, their algebraic sum is always zero.

//This is end of general discussion on KVL, or Kirchhoff’s Voltage Law. Next we see their implementation in circuit analysis.