## Thursday, August 11, 2016

### Kirchhoff's Laws and Explanation

Kirchhoff’s First Law

Current is defined as the rate of flow of charge. To know the flow of current under given voltage and resistance, we can use Ohm’s law. But when circuit becomes little complicated, it is difficult to find the current at a given junction and point. To simplify that we need to use Kirchhoff rules. There are two laws. One regarding charge conservation and other regarding the conservation of voltage.

According to Kirchhoff’s first law, the sum of the charges coming towards a junction is equal to the sum of the currents leaving the junction. This is nothing but conservation of charge that charge is neither created nor destroyed and it just flows from one place to other.

Currents coming towards the junction shall be treated as positive and currents leaving the junction shall be treated as negative. It is conventional consideration to understand the first law.

It is also called as Kirchhoff’s current law.

Kirchhoff’s second law

This law is called Kirchhoff’s voltage law. This is about conservation of voltage in the closed loop or circuit. According to this rule, the voltage available in the circuit through a cell in the form off EMF is distributed over all the elements in the circuit. Thus the sum of potential drop across all the electrical elements is equal to the EMF in the circuit.

To apply the second law, we shall follow certain convention. First this can be applied only to a closed loop or closed circuit but not to any open circuit. The completion of charge flow can happen only with the closed circuit but not in any open circuit.

We also shall choose either clock wise or anti clock wise direction in any closed loop.

If there are multiple loops in a given problem, we shall not change this direction from loop to other and we shall use the same though out the problem.

In the path that we have chosen, if we get first negative plate of the battery and then positive plate of the battery, then we shall consider the EMF as positive and vice versa.
If the current in any electric element is along the same direction that we have chosen, we shall treat the potential drop across the element shall be treated as negative and vice versa.

In a following circuit, we have drawn a electric circuit and applied the law as shown in the diagram below.

Problem and Solution

This problem is based on Kirchhoff voltage law. As per this law the sum of EMF’s in a closed circuit is the sum of potential drops across different elements in the closed circuit. We need to find the current across a given element.

It can be easily solved by taking all the proper sign conventions into consideration as shown below.

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