Question

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

Answer 1

Applying KVL in loop $BCD$ ,
$-i_{1}\times 2+10+5=0\Rightarrow i_{1}=7.5A$
Applying KVL in loop $DEB$ ,
$5+1\times \left(i_{2} + i_{3}\right)+2i_{2}=03i_{2}+i_{3}=-5\ldots \left(1\right)$
Applying KVL in loop $ABCDA$ ,
$-2\times \left(i_{4} - i_{3}\right)+5-i_{1}\times 2+10=0$
$\Rightarrow -2\left(i_{4} - i_{3}\right)+5-2\times 7.5+10=0\Rightarrow i_{4}-i_{3}=0\ldots \left(2\right)$
Applying KVL in loop $AFEB$ ,
$10-2\times i_{3}+10-1\times \left(i_{2} + i_{3}\right)-5+2\times \left(i_{4} - i_{3}\right)=0\Rightarrow 3i_{3}+i_{2}=15\ldots \left(3\right)$
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 $5.$