Question

State and explain Kirchoff’s laws for electrical networks.

Answer 1

Explanation of Kirchhoff's Law

Kirchhoff's 1st Law :- Kirchhoff's first law define as In a circuit,  the algebraic sum of of the current,which is meeting at any junction or terminal is equal to zero.
Refer to the attachment. as there 5 junctions were distinguished .  Meeting at the terminal O.
Let here 
$I_{1} ,I_{2} , I_{3} ,I_{4} , I_{5}$ is the current which passes through the conductor .
Hence we know that by Kirchhoff's law :-
The current which entering in a terminal = Current leaves the terminal.

 $I_{1} + I_{4} + I_{5} = I_{2} + I_{3}$


Kirchhoff's 2nd Law :-
Refer to the second attachment, 
Simply it is applicable for the conservation of energy at any closed circuit.
as V=IR
 Kirchhoff's voltage law is define as for the algebraic sum for product of current & resistance in any closed circuit  is equal to the algebraic sum of electromagnetic force (emf) . or( ∑V = 0) 

$I_{1} R_{2} + I_{2} R_{3} + I_{2} r_{2} + I_{4} R_{6} + I_{1} r_{1}+ I_{1} R_{1} = E_{1} - E_{2}$
The following equation is clearly determined , if you see as the closed loop ABEFA . It is the combination of All the loop's . 
 Also the -ve sign indicate here that the current is in the anti-clockwise direction.



Hope it Helps.

Answer 2

Kirchhoff's Laws :

Kirchhoff's Law or rules are useful for the analysis of complicated electrical circuits.

There are two laws :
1. Kirchhoff's First law 
2. Kirchhoff's Second law 

1. Kirchhoff's First Law[ Junction law or current law ]
" In any closed electrical network, the algebraic sum of currents meeting at a junction is equal to zero."
∑I=0

Consider a junction O at which five conductors meet.Let I1,I2,I3,I4 AND I5 be the currents in these conductors.
By conventions , currents in these conductors towards junction is taken as positive and current leaving junction is taken as negative.
At junction O:
I1-I2+I3-I4+I5=0
or
I1+I3+I5=I2+I4

Thus, " Kirchhoff's law can also be stated as " At any junction in a closed electrical network, the sum of currents entering the junction is equal to sum of current leaving the junction"

Kirchhoff's first  law is based on law of conservation of charge 

2.Kirchhoff's second Law[ Loop rule or mesh rule]:
" The algebraic sum of the emf's and the charges in potential around any closed loop or mesh in an electrical network is zero"
∑ε+IR=0

Consider a closed electric circuit containing two ells of emf's ε1 and ε2 and 3 resistors R1,R2, and R3.
By applying second law to the loop ABEFA
-I2R2-I1R1+ε1=0
I1R1+I2R2=ε1

Applying second law to loop BCDEB,
-ε2-I3R3+I2R2=0
-I3R3+I2R2=ε2

Sign conventions to be followed while applying the Kirchhoff's second law :

1. The emf of a cell is taken positive if one moves in the direction of increasing potential[ from negative terminal to positive terminal ] and  The emf of a cell is taken negative  if one moves in the direction of decreasing  potential[ from positive terminal to   negative terminal ].

2. The product of current and resistance is taken as negative if one moves in the direction of current and it is taken as positive if one moves in a direction opposite to the current.
Kirchhoff's second law is based on law of conservation of energy.