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Kirchhoff's Current Law (KCL)
Kirchhoff’s current law (or Kirchhoff’s current rule) 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 the figure, we see that i1 is the only current flowing into the node.
However, there are three paths for current to leave the node, and these
currents are represented by i2, i3, and i4.
Once charge has entered into the node, it has no place to go except to
leave: this is why we speak about 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,
i1  i2  i3  i4
i1
Node
i4
i2
i3
Bringing everything to the left side of the above equation, we get
i1  i2  i3  i4  0
Then, the sum of all the currents is zero. This can be generalized as follows
i  i
in
out
0
1
Kirchhoff's Voltage Law (KVL)
R1
Kirchhoff's Voltage Law (or Kirchhoff's Loop Rule) is a
result of the conservation of energy. It states that the
total voltage drops 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
V  0
VA
VB
R3
R2
Loop 1
Loop 2
In the figure the sum of the voltage drops around loop 1 should be zero, as in loop 2.
Furthermore, the voltage drops around the outer part of the circuit (including both loops) should
also be zero.
Once we have chosen a direction (clockwise or counterclockwise) to go around a loop, we
will adopt the convention that the potential drop going from point i to point j is given by
If Vi > Vj the potential drop Vij
i
i
is positive, which means that
the energy diminishes in that
V
part of the circuit when i
positive charges go from point
j
i to point j (the energy is R
dissipated in a resistence, or
Vij  V  0
j
the energy of the charges
drops across a source of Vij  i  R  0
voltage).
If Vi < Vj the
potential drop Vij is
negative (potential
gain), which means
that the energy
increases in that
part of the circuit
when
positive
charges go from
point i to point j
Vij  Vi  V j
j
j
V
i
i
R
i
Vij  V  0
Vij  i  R  0
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