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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