Question

In the Fig. find $I,R,{ϵ}_1$ and ${ϵ}_2$

• A. $8A,9\Omega ,54V,36V$
• B. $8A,9\Omega ,36V,54V$
• C. $9A,8\Omega ,36V,54V$
• D. none of these

Answer 1

The correct option is B $8A,9\Omega ,36V,54V$

Redrawing and labeling the diagram as shown in figure.
Applying Kirchhoff's voltage law in loop ABFG,
$2R+{ϵ}_1-{ϵ}_2=0$
$2R+{ϵ}_1={ϵ}_2$...................(1)
Applying Kirchhoff's voltage law in loop BCDH
$3\left(4\right)+I\left(3\right)-{ϵ}_1=0$
$3I+12={ϵ}_1$...................(2)
Applying Kirchhoff's voltage law in loop ACEG
$2R+3\left(4\right)-5\left(6\right)=0$
$2R=30-12$
$2R=18$
$R=9\Omega$......................(3)
Applying Kirchhoff's current at junction D
$3+5=I$
$I=8A$...................(4)
Using (4) in (2), we get
$3\left(8\right)+12={ϵ}_1$
${ϵ}_1=36V$..........................(5)
Using (5) and (3) in (1), we get
$2\left(9\right)+36={ϵ}_2$
${ϵ}_2=54V$........................(6)