KIRCHHOFF'S LAWS:
Kirchhoff's laws are classified
in to two types
1)Kirchhoff's first law (or) Kirchhoff's current law (or) Kirchhoff's
point law.
2)Kirchhoff's second law (or) Kirchhoff's voltage law (or) Mesh law (or)
Loop law.
1)
Kirchhoff's current law(KCL): The algebraic sum of the current's
meeting at a point (or) node (or) junction in an electric network is zero.
(or)
The sum of incoming current's are equal to the sum of outgoing current's
at a point (or) junction in an electric network.
Explanation:
Let there be a Five conductors carrying
current's i1,i2,i3,i4,i5 meeting at junction point 'o'
as shown in figure. The arrow heads shows the direction of the current flowing.
Assuming i3 and i5 be the current flowing
towards the junction 'o'(i.e. incoming current's) are taken as positive i1,i2 and i4
be the current flowing away from the junction(i.e. outgoing current's) are
taken as negative.
Applying KCL to junction 'o' the figure get
i3+i5=i1+i2+i4
i3+i5-i1-i2-i4=0
i.e. Sum of incoming current's=Sum of outgoing current's
2)KIRCHHOFF'S
VOLTAGE LAW:
In a closed path (or)mesh the algebraic sum of the products of current's
and resistance in each of the conductor plus the algebraic sum of the EMF's in
that path is equal to zero.
Mathematically
∑V+∑EMF=0
Sign
conversion of EMF's and voltage drop:
In applying KVL in a closed circuit (or) mesh it is very important to
assign proper to the EMF's and voltage drops in the closed circuit. The
following sign conversion may be followed a rise in potential should be
considered as positive by fall in potential should be considered as negative.
Sign
conversion for EMF's:
If we move from
negative terminal to the battery to the positive terminal there is a rise in
potential and the EMF should be assigned positive sign on the another hand if
we move from the positive terminal of the battery to the negative terminal.
Note:
It should be noted that is independent of the direction of current through that
branch.
Sign
conversion for voltage drop:
When current flowing through a resistance 'R' there is a voltage drop
across it if we move through the resistor in the same direction as the current
there is a fall in potential because current floes from higher potential to
lower potential hence the voltage drop is given as negative sign and the
another hand if we go in a direction opposite to that of drop there is a rise
in potential and the voltage drop is given as positive sign.
Note:
It should be noted that sign of voltage drop depends upon the direction of
current and is independent of the direction of the polarity of the EMF in the
circuit under consideration .
Steps
to solve circuit by Kirchhoff's laws:
Step1:Assume
unknown current's in various branches of a given circuit.
Step2:Mark
the direction of flow of current for the assumed current's by applying KCL.
Step3:Choose
as many number of closed loop's as the number of unknown quantities.
Step4:Applying
KVL to the closed loop's and proper the equation's.
Step5:Solve
the equation's to find the unknown quantities.
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