Two cells of emf E_1 and E_2 and internal resistances r_1 and r_2 are connected in parallel, with their terminals of the same polarity connected together. Obtain an expression for the equivalent emf of the combination.

CBSE Class 12 Physics 2023 Outside Delhi Set 2 Paper

Question : 13

Total: 13

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.

Solution: 👈: Video Solution

Terminal p.d of 1‌st ‌ cell,
V‌=E1−I1r1
∴‌‌I1‌=‌

E1−V

Terminal p.d of 2‌nd ‌ cell,
‌V‌=E2−I2r2
‌∴‌I2‌=‌

E2−V

‌‌ Now, ‌‌I‌=I1+I2
‌‌ Or, ‌‌I‌=‌

E1−V

+‌

E2−V

‌‌ Or, ‌‌Ir1r2‌=r2(E1−V)+r1(E2−V)
‌‌ Or, ‌‌V(r1+r2)‌=E1r2+E2r1−Ir1r2
‌‌ Or, ‌‌V‌=‌

E1r2+E2r1

r1+r2

−I‌

r2r1

r1+r2

Comparing with V=E−Ir
Equivalent emf =E=

E1r2+E2r1

r1+r2

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