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ELECTRICAL STUDY MATERIAL | KCL – KVL

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KIRCHHOFF’S CURRENT LAW | KIRCHHOFF’S VOLTAGE LAW | KCL | KVL

KIRCHHOFF’S CURRENT LAW:

Kirchhoff’s current law may be stated as follows.  The sum of the currents entering a node is equal to the sum of the currents leaving that node. This means that the algebraic sum of the currents meeting at a node is equal to zero.

Applying the law to the node shown in Fig. we see that

KCL-KIRCHOFF'S CURRENT LAW

I1 + I2 + I3  =  I4 + I5

Rearranging,

I1 + I2 + I3 – I4 – I5=0

KIRCHHOFF’S VOLTAGE LAW:

Kirchhoff’s voltage law may be stated as follows.  The sum of the voltage sources around any closed path is equal to the sum of the potential drops around that path. This means that the algebraic sum of all the potential differences around any closed path is equal to zero. The important points to remember are (1) the path must be closed and (2) it is an algebraic sum. Always decide upon a positive direction (say clockwise) for a trip around the path:

Potential differences in that direction are then positive and those in the opposite direction are negative.

Applying the law to the circuit of Fig.  We see that for the closed path containing the nodes 6, 1, 2, 5 and 6, taking the clockwise direction to be positive,

I3R3 – V + I1R1 = 0

KVL-KIRCHOFF'S VOLTAGE LAW

Rearranging we obtain

V = I1 R1 + I3 R3                        ——–(1)

For the closed path containing the nodes 5, 2, 3, 4 and 5, taking the clockwise direction to be positive,

I1 R1 + V – I2 R2 = 0

Rearranging we get

V =  I1R1 + I2R2                         ——–(2)

Finally, for the closed path containing nodes 6, 1, 2, 3, 4, 5 and 6, taking the clockwise  direction to be positive,

I3R3 – I2R2 = 0

From which

I3R3 = I2R2                                 ——–(3)

Note that Equation (3) is not independent because it could have been obtained from  Equations (1) and (2) simply by equating their right-hand sides.

KIRCHHOFF’S CURRENT LAW | KIRCHHOFF’S VOLTAGE LAW | KIRCHHOFF’S LAWS | KCL | KVL

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