Electrostatics - Electric Measurement Laws, Kirchhoff Laws

Electric Measurement Laws

Kirchhoff in 1942 put forwards the following two laws to solve the complicated circuits* these laws are simply the expressions of conservation o electric charge and of energy. These laws were stated as follows:
    
Kirchhoff’s first law or Kirchhoff’s junction law or Kirchhoff’s current law. 

It states that the algebratic sum of the currents meeting at a junction in a closed circuit is zero.

Krirchhoff’s first law supports law of conservation of charge. This is because a point in a circuit cannot act as a source or sink of charge. Kirchhoff first law is also known as Kirchhoff’s current law.

Consider a junction O in the electrical circuit at which the farce conductors are meeting kept I₁, I₂, I₃, I₄, and I₅, be the current in these conductors in directions 

Let us adopt the following sign convention the current flowing in a conductor towards the junction is taken as positive and the current flowing away from the junction is taken as negative.

According to Kirchhoff’s first law at junction 0 (-I₁) + (-I₂) + I₃ + (-I₄) + I5 = 0

Or – I₁ – I₂ + I₃ – I₄ + I₅ + 0

∑I = 0

Kirchhoff’s second law or Kirchhoff’s loop law or Kirchhoff’s voltage law.

It states that the algebratic sum of charges in potential around any closed path of electric circuit (or closed loop) involving resistors and cells in the loop is zero, ∑?V = 0.

Kirchhoff’s second law supports the law of conservation of energy the net charge in the energy of a charge, after the charge completes a closed path must be zero. in fact kirchhoff’s second law follows from the fact that the electrostatic force is a conservative force and work done by it in any closed path is zero. 

Consider a closed electrical circuit as shown in containing two cells of ε₁ and ε₂ and three resistors of resistances R₁, R₂, and R₃, 

We adopt the following sign convention:

Traverse closed path of a circuit in clockwise or ant clock wise direction.

The of a cell is taken negative if one moves in the direction of increasing potential from negative pole to positive pole through the cell and is taken positive if one moves in the direction of decreasing potential (form positive pole to negative pole) through the cell. It means while traversing a lop if negative pole of the cell is encountered first then it is negative otherwise positive.

The product of resistance and current in an arm of the circuit is taken positive if the direction of current entreat arm is in the same sense as one moves in a closed path and is taken ne3gatice if the direction of current path and is taken negative if the direction of current I in that arm is apposite to the sense as one moves in a closed path. 

Let us apply Kirchhoff’s second law to the closed path ABEFA, we have

I₃ R₂ + I₁ RI – ε₁ = 0

Or ε₁ = I₁ R₁ + i₃ R₂

Similarly, for closed path ABCDEFA, we have 

ε₂ – I₂ R₃ + I1 R1 – ε1 = 0

Or ε1 – ε2 = I1 R1 – I2 R3

∑ε = ∑IR

Difference between Kirchhoff’s I and II laws 

First law	Second law
This law supports the law of conservation of charge	This law supports the law of conservation of energy.
According to this law ∑I = 0	According to this law ∑ε = ∑ I R
This law can be used in open and closed circuits	This law can be used in a closed circuit.

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