Question

The current through battery between A & B is?

• A. $0.4$A
• B. $0.8$A
• C. $0.6$A
• D. $1$A

Answer 1

The correct option is C $0.6$A

Using Kirchhoff's law for loop $ABVHA$

$2-2I_1-2I=0$

$⟹2=2(I_1-I)$

$⟹I_1=1-i\to \left(1\right)$

Using Kirchhoff's law for loop $AHVGPBA$

$2I+2+2I_2-2=0$

$⟹I=-I_2\to \left(2\right)$

Using Kirchhoff's law for loop $AHVGUCPBA$

$2I+2+2I_3-2-2=0$

$I+I_3=1$

$⟹I_3=1-I\to \left(3\right)$

Using Kirchhoff's law for loop $AHVGUFQCPBA$

$⟹2I+2+2+I_4\left(2\right)-2-2=0$

$I_4=-I\to \left(4\right)$

Using Kirchhoff's law for loop $AHUGUFTDQCPBA$

$⟹2I+2+2+I_5\left(2\right)-2-2-2=0$

$I_5=-I\to \left(5\right)$

Using Kirchhoff's law for loop $AHUGuFTERDQCPBA$

$⟹2I+2+2+2+2(I-I_1-I_2-I_3-I_4-I_5)-2-2-2=0$

$I_1+I_2+I_3+I_4+I_5=0\to \left(6\right)$

Using equations $\left(1\right),\left(2\right),\left(3\right),\left(4\right),\left(5\right)$ in $\left(6\right)$

$⟹1-I-I+1-I-I+1-I=0$

$⟹5I=3⟹I=\frac{3}{5}A$

Current through arm $AB⟹I=\frac{3}{5}=0.6A$