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Two Cells of Emfs E1 and E2 and Internal Resistances R1 and R2 Are Connected in Parallel. Derive the Expression for the (I) Emf and (Ii) Internal Resistance of a Single Equivalent Cell Which Can Replace this Combination. - Physics

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Two cells of emf E1 and E2 and internal resistances r1 and r2 are connected in parallel. Derive the expression for the (i) emf and (ii) internal resistance of a single equivalent cell which can replace this combination.

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E1, E2 = Emf of two cells

r1, r2 = Internal resistances of cell

I1, I2 = Current due to the two cells

Terminal potential difference across the first cell is

V = E1 − I1r1


For the second cell, terminal potential difference will be equal to that across the first cell. So,

V = E2I2r2


Let E be effective emf and r is effective internal resistance. Let I be the current flowing through the cell.





Comparing the equation with V=EIr, we get



Concept: Induced Emf and Current
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