When the circuit is complicated to find current Kirchhoff’s laws are formulated.
i)Kirchhoff`s First Law (Junction Law or Current law) : It states that the sum of the currents flowing into a junction is equal to the sum of the currents flowing out of the junction.
Or
“The algebraic sum of currents at a junction is zero”. ∑I =0
Distribution of current at a junction in the circuit
I₁+I₂=I₃+I₄ or I₁+I₂-I₃-I₄ =0
If we take currents approaching point A in Fig as positive and that leaving the point as negative, then the above relation may be written as
I₁+I₂+(-I₃)+(-I₄) =0
Note: Thus, Kirchhoff’s first law is accordance with law of conservation of charge, since no charge can accumulate at a junction.
ii) Kirchhoff`s Second Law (Loop Law or Potential law) : Kirchhoff’s second law states that the algebraic sum of changes in potential around any closed loop is zero.
(Kirchhoff’s second law) can be expressed as . ∑v =0
In terms of potential drops and emf's, the law is expressed as ∑v +∑E =0
Sign conventions:
(a)The change in potential in traversing a resistance in the direction of current
is –IR while in the opposite direction +IR as shown in the figure.
(b)The change in potential in traversing an emf source from negative to positive is +E while in the opposite direction –E irrespective of the direction of current in the circuit as shown in the figure.
EX. 40: Solve for current values in figure.
Sol.Applying Kirchhoff’s first law at the junction B we have I₁+I₂=I₃..... (1)
Applying Kirchhoff’s second law to loop ABEFA
–12 + i₂ x1.5 –i₁ x 1 + 8 = 0
I₁ – 1.5 I₂ = – 4........ (2)
From loop BCDEB
– (i₂ x 1.5) – (I₃ x 9) + 12 = 0
1.5i₂ + 9i₃ = 12....... (3)
on solving I₁ = – 1A and I₃ = 1 A, i₂ = 2A
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