According to this law in any closed circuit or mesh the algebraic sum of e.m. f.s. acting in that circuit or mesh is equal to the algebraic sum of the products of the currents and resistances of each par of the circuit.

If the circuit shown in is considered then according to Kirchhoff’s second law,

In mesh AFCBA  E₁ = R₁ (I₁+I₂) + R₂ (I₁+I₂) + R₅R₁
               or        E₁ = (R₁+R₂)(I₁+I₂) + R₅R₁
In mesh FEDCF - E₂ = -R₃ I₂ - R₄ I₂ - R₃ (I₁+I₂) - R₁ (I₁+I₂)
               or        E₂ = R₃ I₂ + R₄ I₂ + (R₁+R₂)(I₁+I₂)
and in mesh AFEDCBA E₁-E₂ = -R₃ I₂ - R₄ I₂ + R₅ R₁
                     or   E₁ - E₂ = R₅ I₂ - (R₃+R₄) I₂  

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