Current Electricity 2 Question 8
8. In the given circuit, the cells have zero internal resistance. The currents (in Ampere) passing through resistances $R _1$ and $R _2$ respectively are
(2019 Main, 10 Jan I)
(a) $0.5,0$
(b) 1,2
(c) 2,2
(d) 0,1
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Solution:
- By Kirchhoff’s loop rule in the given loop $A B E F A$, we get
$$ \begin{aligned} & 10-\left(I _1+I _2\right) R _1=0 \\ & \Rightarrow \quad 10-\left(I _1+I _2\right) 20=0 \\ & \text { or } \quad I _1+I _2=\frac{1}{2} \end{aligned} $$
and from loop $B C D E B$, we get
$$ \begin{array}{rlrl} & & 10-\left(I _1+I _2\right) R _1-I _2 R _2 & =0 \\ \Rightarrow & 10-\left(I _1+I _2+I _2\right) 20 & =0 \\ \Rightarrow & & I _1+2 I _2 & =\frac{1}{2} \end{array} $$
From Eqs. (i) and (ii), we get
$$ I _2=0 \text { and } I _1=0.5 A $$
