Question

What is the current flowing in arm AB?

• A. $\frac{35}{4}A$
• B. $\frac{13}{7}A$
• C. $\frac{5}{7}A$
• D. $\frac{7}{5}A$

Answer 1

Answer: (B)

LeT $i_1,i_2$ be current in the two loops of the given circuit then
Appiying Kirchhoff's Iaw to Ioop I, we get
$(\Sigma iR=V)$
$8i_1+2(i_1+i_2)=10$
$\Rightarrow 10i_1+2i_2=10$
$\Rightarrow 5i_2+i_2=5......(i)$
Applying Kirchhoff law to loop 2, we get
$4i_2+2(i_1+i_2)=8$
$\Rightarrow 6i_2+2i_2=8$
$\Rightarrow i_1+3i_2=4.....(ii)$
From Eqs. (i) and (ii), we get
$i_1=\frac{11}{14}A,i_2=\frac{15}{14}A$
Hence current flowing is arm AB is
$i_1+i_2=\frac{11}{14}+\frac{15}{14}=\frac{26}{14}=\frac{13}{7}A$