Kirchhoff's first law and Kirchhoff's Second law

 Kirchhoff's first law 

• the algebraic sum of the currents meeting at a junction in a closed electric circuit is zero,          i.e.,  𝜮I= 0
• Consider a junction O in the electrical circuit at which the five conductors are meeting. Let I_1, I_2,  I_3,  I_4, and I₅ be the currents 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 O                                                                  

               

                 (-I₁ ) + (-I₂ ) + I₃  + (-I₄ ) + I₅  = 0
                or -I₁  +  -I₂ + I₃  -I₄  + I₅ = 0
                or  𝜮I = 0

• I₃  + I₅ = I₁ + I₂ + I₄   i.e., the total current flowing towards the junction is equal to the total current flowing out of the junction.
• Current cannot be stored at a junction. That is, there is no point/ junction in a circuit that can act as a source or sink of charge. 
• Kirchhoff's first law supports the law of conservation of charge.

Kirchhoff's Second law  

• The algebraic sum of changes in potential around any closed path of an electric circuit (or closed-loop) involving resistors and cells in the loop is zero, i.e.,  𝜮∆ V= 0.
• In a closed loop, the algebraic sum of the EMFs and algebraic sum of the products of current and resistance in the various arms of the loop is zero, i.e., 𝜮ε   + 𝜮 IR  = 0.
• Kirchhoff's second law supports the law of conservation of energy, i.e., the net change in the energy of a charge, after the charge completes a closed path must be zero.
• 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.
• Traverse a closed path of a circuit once completely in a clockwise or anticlockwise direction.

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