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प्रश्न
Two cells of emf E1 and E2 and internal resistances r1 and r2 are connected in parallel, with their terminals of the same polarity connected together. Obtain an expression for the equivalent emf of the combination.
उत्तर
Two cells of emf ε1 and ε2 and internal resistance r1 and r2 connected in parallel,
Total current will be I = I1 + I2 ..............(i)
Let V = Potential difference between A and B. ε1
For cell ε1,
Then `V = ε_1 - I_1r_1`
`I_1 = ((ε_1 - V))/r_1`
Similarly, for cell ε2, I2 = `((ε_2 - V))/r_1`
Putting these values in equation (i),
I = `((ε_1 - V))/r_1 + ((ε_2 - V))/r_2`
I = `(ε_1/r_1 + ε_2/r_2) - V(1/r_1 + 1/r_2)`
or V = `((epsilon_1r_2 + epsilon_2r_1))/((r_1 + r_2)) - I((r_1r_2)/(r_1 + r_2))` ...........(ii)
Comparing the above equation with the equivalent circuit of emf 'εeq' and internal resistance 'req' then,
V = `epsilon_{eq} - Ir_{eq}` ............(iii)
Then
so, the equivalent emf will be `epsilon_{eq} = ((epsilon_1r_2 + epsilon_2r_1))/((r_1 + r_2))`.
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