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## Kirchhoff's current law (KCL) and Kirchhoff's voltage law(KVL)

This page on KCL vs KVL mentions basic difference between Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL).

There are two Kirchhoff laws namely KCL and KVL as mentioned. KCL deals with flow of current while KVL deals with voltage drop in closed network.

### Kirchhoff Current Law (KCL) The KCL states that "algebraic sum of currents at any node of a circuit is zero".
⇒ i1 + i2 - i3 - i4 - i5 = 0

In other words, algebraic sum of currents entering a node must be equal to algebraic sum of currents leaving a node.
⇒ i1 + i2 = i3 + i4 + i5

Example: Given i1 = 10, i2 = 6 and i5 = 4, Find other currents ( i3, i6, i7)
By observation and using KCL, i1 = i7 and hence i7 = 10

At node A, applying KCL, i1 = i2 + i4
⇒ 10 = 6 + i4
⇒ i4 = 4

At node B, applying KCL, i2 = i3 + i5
⇒ i3 = i2 -i5 = 6 -4 = 2

At node C, applyign KCL, i7 = i5 + i6
⇒ i6 = i7 - i5 = 10-4 = 6 Amp

### Kirchhoff Voltage Law (KVL) The KVL states that "algebraic sum of voltages (or voltage drops) in any closed path of network which is traversed in a single direction is zero." As per network depicted in the figure-2 and as per KVL applying in anti-clockwise,
⇒ -V1 + (-V2) + i*R1 + i*R2 = 0