Question

In the given circuit diagram the current through the $1\Omega$ resistor is $I$ . Find the value of $2I$ (in $A$ )?

Answer 1

Answer: 5

Applying KVL in loop $BCD$ ,
$-i_1\times 2+10+5=0\Rightarrow i_1=7.5A$
Applying KVL in loop $DEB$ ,
$5+1\times \left(i_2+i_3\right)+2i_2=03i_2+i_3=-5\dots \left(1\right)$
Applying KVL in loop $ABCDA$ ,
$-2\times \left(i_4-i_3\right)+5-i_1\times 2+10=0$
$\Rightarrow -2\left(i_4-i_3\right)+5-2\times 7.5+10=0\Rightarrow i_4-i_3=0\dots \left(2\right)$
Applying KVL in loop $AFEB$ ,
$10-2\times i_3+10-1\times \left(i_2+i_3\right)-5+2\times \left(i_4-i_3\right)=0\Rightarrow 3i_3+i_2=15\dots \left(3\right)$
Solving equation $1$ and $3$ simultaneously we get,
$i_2=-\frac{15}{4}A\text{and }{i}_3=\frac{25}{4}A$
Now current in $1\Omega$ resistance is $i_2+i_3=\frac{-15+25}{4}=\frac{5}{2}A$
Therefore, the answer is $5.$