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Kirchoff’s first law

This law is also known as junction rule or current law (KCL). According to it, the algebraic sum of currents meeting at a junction is zero, i.e., ∑i = 0.
 
In a circuit, at any junction the sum of the currents entering the junction must equal the sum of the currents leaving the junction, i.e., i1 + i3 = i2 + i4.
 
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Fig. 24
 
This law is simply a statement of ‘conservation of charge.

Kirchoff’s second law

This law is also known as loop rule or voltage law (KVL) and according to it, ‘the algebraic sum of the changes in potential in complete traversal of a mesh (closed loop) is zero’, i.e., ∑V = 0
  • This law represents ‘conservation of energy’.
  • If there are n meshes in a circuit, the number of independent equations in accordance with loop rule will be (n – 1).

Sign convention for the application of Kirchoff’s law

For the application of Kirchoff’s laws following sign conventions are to be considered:
  • The change in potential in traversing a resistance in the direction of current is –iR while in the opposite direction +iR (Fig. 25).
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Fig. 25
  • The change in potential in traversing an emf source from negative to positive terminal is +E, while in the opposite direction –E, irrespective of the direction of current in the circuit (Fig. 26).
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Fig. 26




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