Question

Three cells of emf’s E₁ , E₂ and E₃ and internal resist are r₁ , r₂ , r₃ and connected in parallel through an external resistance R. Calculate the current flowing through each cell.

Answer 1

Suppose i₁ , i₂ and i₃ be the currents in given three cells and r be this current through external resistance R. Applying Kirchoff’s first law to the point, we have A

i = i₁ + i₂ + i₃ .....(1)

Applying second law to the mesh E₁ A R B E₁ , we have

i₁ r₁ + iR = E₁ .....(2)

Similarly, i₂ r₂ + iR = E₂ (Mesh E₂ A R B E₂) .....(3)

and i₃ r₃ + iR = E₃ (Mesh E₃ A R B E₃) .....(4)

Divides equation (2) by r₁ , equation (3) by r₂ and equation (4) by r3 and adding we get