Current Electricity 2 Question 28

28. In the circuit shown in figure $E, F, G, H$ are cells of emf 2, 1 , 3 and $1 V$ respectively, and their internal resistances are 2, 1, 3 and $1 \Omega$ respectively. Calculate

$(1984,4 M)$

(a) the potential difference between $B$ and $D$ and

(b) the potential difference across the terminals of each cells $G$ and $H$.

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Solution:

  1. Applying Kirchhoff’s second law in loop $B A D B$

$$ 2-2 i _1-i _1-1-2\left(i _1-i _2\right)=0 $$

Similarly applying Kirchhoff’s second law in loop $B D C B$

$$ 2\left(i _1-i _2\right)+3-3 i _2-i _2-1=0 $$

Solving Eqs. (i) and (ii), we get

(a) Potential difference between $B$ and $D$.

$$ \begin{aligned} V _B+2\left(i _1-i _2\right) & =V _D \\ \therefore \quad V _B-V _D=-2\left(i _1-i _2\right) & =\frac{2}{13} V \end{aligned} $$

(b)

$$ \begin{gathered} V _G=E _G-i _2 r _G=3-\frac{6}{13} \times 3=\frac{21}{13} V \\ V _H=E _H+i _2 r _H=1+\frac{6}{13} \times 1=\frac{19}{13} V \end{gathered} $$



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