Kvl And Kcl

KCL

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 1, 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

Kirchhoff's
Voltage Law


Kirchhoff's Voltage Law (or Kirchhoff's Loop Rule) is a
result of the electrostatic field being conservative. It states that the
total voltage around a closed loop must be zero. If this were not the case,
then when we travel around a closed loop, the voltages would be indefinite.
So

In Figure 1 the total voltage around loop 1 should sum to zero, as does
the total voltage in loop2. Furthermore, the loop which consists of the
outer part of the circuit (the path ABCD) should also sum to zero.