1i2i

3i

Current entering the node is positive and leaving the node is negative

( ) 0 1 2 3i i i 0 1 2 3i i i

Current entering the node is negative and leaving the node is positive

( 0) ( ) 1 2 3i i i 0 1 2 3i i i

Note the algebraic sign is regardless if the sign on the value of the current

Kirchhoff's Current Law ( KCL):

The algebraic sum of all the currents at any node in a circuit equals zero.

Figure 1.14 Illustration of Kirchhoff

’s current law (KCL).

( ) ( ) 0 1 4 52 3i i i i i

Entering currents a nodecur Leavrents a no in de g

1 5 43 2 i i i i i

KCL also applies to larger and closed regions of circuit called supernodes

2 6 9 10i i i i

Example 1.3: Determine the currents ix, iy and iz

KCL at node dix+3=2ix = 2-3 = -1A

KCL at node aix+ iy +4 = 0iy = -3A

KCL at node b4 + iz + 2 = 0iz = -6A

We could have applied KCL at the supernode to getiy + 4A + 2A = 3AThus iy = -3

Figure 1.17Example 1.4.

Kirchhoff Voltage Law (KVL)

The algebraic sum of all the voltages around any closed path in a circuit equals zero.

First we have to define a closed path

+

a b c

def

A closed path or a loop is defined as starting at an arbitrary node, we trace closed path in a circuit through selected basic circuit elements including open circuit and return to the original node without passing through any intermediate node more than once

abea bceb cdec aefa abcdefa

Kirchhoff Voltage Law (KVL)

The algebraic sum of all the voltages around any closed path in a circuit equals zero.

The "algebraic" correspond to the reference direction to each voltage in the loop.

Assigning a positive sign to a voltage rise ( to + )

Assigning a negative sign to a voltage drop ( to )

5 V +

2 W 3 W

6 W 5 W

+ 1v +

3v+

2v

+

4v

Assigning a positive sign to a voltage drop ( to )

Assigning a negative sign to a voltage rise ( to )

OR

Example

5 V +

2 W 3 W

6 W 5 W

+ 1v +

3v+

2v

+

4v

Loop 1 0 1 2 5v v

Loop 2 0 43 2v v v

We apply KVL as follows:

Figure 1.23 Another example of the application of KVL.