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  • Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ωrespectively, are connected in parallel with the positive end of 10V battery connected to negative pole of 2V battery (Figure).

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

Answers (1)

Kirchoff's Junction Law at C: I_1=I_2+I_3

Kirchoff's Loop Law for efbae:10-I_1\times 10-I -3\times R=0

10-10I_2-(R+10)I_3=0

Kirchoff's Loop Law for cbadc:- 2+5I_2-I_3R=0

(10-10I_2-(R+10)I_3)+(-2+5I_2-I_3R)\times 2=0

6-I_3R+10-2I_3R=0

6=3I_3R+10I_3

I_3=\frac{6-3I_3R}{10}

Veff & Reff will fulfil the following:

V_{eff}-I_3(R+R_{eff})=0

R_{eff}=\frac{1}{\frac{1}{10}+\frac{1}{15}}=\frac{10}{}3

V_{eff}-I_3\left (R+\frac{10}{}3 \right )=0

V_{eff}=I_3R+I_3\times \frac{10}{}3

V_{eff}=I_3R+\frac{6-3I_3R}{10}\times \frac{10}{}3=I_3R+6-\frac{3I_3R}{}3=2V

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