Question

State the two Kirchhoff's rules used in electric networks. How are there rules justified?

Answer 1

Kirchhoff's first rule ( Kirchhoff's Current Law or KCL or Junction Rule) :

It state that, the sum of the currents flowing towards a junction is equal to the sum of currents leaving the junction.

This is in accordance with the conservation of charge which is the basis of Kirchhoff's current rule.

In fig(i), $I_1,I_2,I_3,I_4$ are currents flowing through the respective wires.

Convention: The current flowing towards the junction is taken positive and the current flowing away from the junction is taken as negative.

Hence, $I_3+(-I_1)+(-I_2)+(-I_4)=0$

"In any electric network, the algebraic sum of currents meeting at a junction is always zero", $\sum I=0$

Kirchhoff's second rule ( Kirchhoff's Voltage Law or KVL Loop rule ) :

It state that the algebraic sum of all potential drops and emfs along any closed path in a network is zero.

OR

The algebraic sum of the emfs in a loop of a circuit is equal to the algebraic sum of the product of current and resistances in it.

Mathematically, the loop rule may be expressed as :

$\sum E=\sum IR$

Kirchhoff's second law express the conservation of energy.

From fig(ii),

For closed loop BACB:

$E_1-E-2=I_1{R}_1+I_2{R}_2-I_3{R}_3$

For closed loop CADC:

$E_2=I_3{R}_3+I_4{R}_4+I_5{R}_5$