Kirchhoff’s rules

Kirchhoff’s rules

In this topic we will discuss about , Kirchhoff’s rule and explanation of  its type.And also we will discuss, how Kirchhoff’s second rule loop rule/ potential rule , support the law of conservation of energy ?

Kirchhoff’s rule 

First rule ( junction rule /current rule ) –  According to this law when current flowing through several wires meet at a point ( junction) the at a junction in closed circuit is always zero .

[ sign convention –  generally when current flows towards the junction is taken positive and when it moves away from the junction is taken negative . ]

As shown in figure,  ‘o’ is the junction then according to Kirchhoff’s law  .

-I1+I2-I3+I4+I5 = 0 …………………..Eq.

Then from the above relation we can say at a junction current entering is equal to current leaving .

Second rule ( loop rule / voltage rule ) – According to this rule for a closed loop the algebraic sum of change in potential must be zero . In another words we can say algebraic sum of potential differences across the cells and product of current and resistance across the resistor should be zero .

[ ***sign convention-  select any point on the closed circuital loop you can move along your desired direction (clock or anti-clock wise direction) , when you reaches to the resistor then see the your moving direction and direction in which current flowing through the circuit the sign of ‘IR’( product of current and resistance ) if it is same the sign will be positive , if it is opposite then sign will be negative . And sign of potential or EMF of the cell will be positive if you touch positive terminal first , and sign will be negative if you touch negative terminal first ].

To understand the loop rule see the following example –

Suppose we have a loop shown in fig;-

from the loop ABCDEFA,     -ε2+ ε1+i2R2 -i1R1=0

or , ε1– ε2= i1R1– i2R2 ……………………..(i)

again from the loop BEDCB ,  ε2-i3R3-i2R2=0

or,  ε2= i3R3+i2R2………………………..(ii)

and from the loop ABEFA, ε1 -i3R3-i1R1=0

or, ε1 =i3R3+i1R1………………………….(iii)

using equations (i),(ii),and (iii) we can find the all unknown quantities.

*** Kirchhoff’s second rule loop rule/ potential rule , support the law of conservation of energy –

In a closed loop the charges calculated around a closed loop in a particular direction due to electrostatic force which is conservative in nature . The work done by the electrostatic force on the circulating charge in a closed loop is zero . Due to it , the net charge in the energy of charge when goes on a closed loop is zero. It means there is no gain in energy  by circulating charges around a closed loop in a particular direction which is law of conservation of energy . Thus Kirchhoff’s supports the law of conservation of energy . ***

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