Two cells of voltage 10V and 2V and internal resistances
Question:

Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively are connected in parallel with the positive end of the 10V battery connected to the negative pole of 2V battery. Find the effective voltage and effective resistance of the combination.

Solution:

Kirchhoff’s law is applied at c, I1 = I + I2

Kirchhoff’s law is applied at efbae, 10 – IR – 10I2 = 0

10 = IR + 10I1

Kirchhoff’s law is applied at cbadc, -2-IR+5I2 = 0

2 = 5I2- RI

I2 = I1 – I

Substituting the values we get

Equivalent internal resistance of the two cells as (10/3) Ohms

Following is the equivalent circuit when the combination of 5 and 10 Ohm are used

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