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 $