Kirchoff's Laws
Category : JEE Main & Advanced
(1) 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. \[\Sigma \,i=0\].
In a circuit, at any junction the sum of the currents entering the junction must equal the sum of the currents leaving the junction. \[{{i}_{1}}+{{i}_{3}}={{i}_{2}}+{{i}_{4}}\]
(ii) This law is simply a statement of "conservation of charge".
(2) 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. \[\Sigma V=0\]
(i) This law represents "conservation of energy".
(ii) If there are n meshes in a circuit, the number of independent equations in accordance with loop rule will be \[(n-1)\].
(3) Sign convention for the application of Kirchoff's law : For the application of Kirchoff's laws following sign convention are to be considered
(i) The change in potential in traversing a resistance in the direction of current is \[-iR\] while in the opposite direction \[+iR\]
(ii) 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.
(iii) The change in potential in traversing a capacitor from the negative terminal to the positive terminal is \[+\frac{q}{C}\] while in opposite direction \[-\frac{q}{C}\].
(iv) The change in voltage in traversing an inductor in the direction of current is \[-L\frac{di}{dt}\] while in opposite direction it is \[+L\frac{di}{dt}\].
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