Question

Using Kirchhoff's rules determine the value of unknown resistance $R$ in the circuit so that no current flows through $4\Omega$ resistance. Also find the potential between $A$ and $D$.

Answer 1

Applying Kirchhoff's second law in closed mesh AFEBA ,

$9-6=I\times 1+I\times 1+4\times 0=0$ (current in $4\Omega$ is given zero)

or $3=2I$

or $I=3/2=1.5A$

now in closed mesh AFEDCBA ,

$9-3=I(1+1)+IR$

or $6=1.5\times 2+1.5R$

or $6=3+1.5R$

or $R=3/1.5=2\Omega$

now from point A to point D , (applying Kirchhoff's law for linear part AFED)

$V_A-I(1+1)=V_D$

or $V_A-V_D=1.5\times 2=3V$