Question

Two cells of emf e1 and e2 internal resistance r1 and r2 connected in parallel.derive expression for emf and internal resistance

Answer 1

NET E. M. F. = (e1/r1 + e2/r2) / (1/r1 + 1/r2)
RESISTANCE = 1/R1 + 1/R2

Answer 2

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Let's make the question somewhat lengthy by adding also find: (ii) Internal resistance of single equivalent cell_(^.^)

Given:

E1 and E2 = emf of two cells

r1 and r2 = internal resistance of cells

l1 and l2 = current due to the two cells

Solution:

Terminal potential difference across the first cell is

V = E1 - l1 r1

=> ɪ1 = E1 - V

r1

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

V = E2 - I2 r2

=> ɪ2 = E2 - V

r1 +r2

Let E be the effective emf and r is effective internal resistance

let l be the current flowing through the cell

l= l1 + l2

=> ɪ = E1 - V + E2 - V

r1 r2

=> ɪ r1r2 = E1r2 + E1r1 - (r1 + r2)

=> V = E1 r2 + E2 r1 - ɪ r1r2

r1 + r2 r1 + r2

Comparing the Equation with V= E-ɪr, we

E = E1 r2 + E2 r1

r1 + r2

=> r = r1 r2

r1 + r2

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