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  • In the series circuit shown, E,F,G,H are cells of emf 2V,1V,3V and 1V respectively, and their internal resistance are 2, 1, 3 and 1 respectivel

In the series circuit shown, E,F,G,H are cells of emf 2V,1V,3V and 1V respectively, and their internal resistance are 2, 1, 3 and 1\Omega respectively.The potential difference between B and D is 
        

Option: 1

\frac{2}{13} V


Option: 2

\frac{3}{13} V


Option: 3

\frac{4}{13} V


Option: 4

\frac{5}{13} V


Answers (1)

best_answer

Let us redraw the circuit. At junction D, we have applied the junction rule, whereby we get current in DB as shown. Loop BADB  
\begin{aligned} & 2 I_1-2+1+I_1+2\left(I_1-I_2\right)=0 \\ & \Rightarrow 5 I_1-2 I_2=1 \\ & \text { Loop DCBD } \\ & -3+3 I_2+I_2+1-2\left(I_1-I_2\right)=0 \Rightarrow 6 I_2-2 I_1=2 \\ & \Rightarrow I_1=\frac{5}{13} A, I_2=\frac{6}{13} A \\ & V_{B D}=2\left(I_1\right)-2+1+I_1=3 I_1-1=3\left(\frac{5}{13}\right)-1=\frac{2}{13} V\end{aligned}

Posted by

himanshu.meshram

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