Question

For the circuit shown in figure, the equivalent resistance between $A$ and $C$ is

• A. $\frac{12}{11}r$
• B. $\frac{13}{11}r$
• C. $\frac{14}{11}r$
• D. $\frac{15}{11}r$

Answer 1

Answer: (D)

At junction $E$ or $F$ :
$I_1+I_3+I_4=I_2-I_3$
or $I_1-I_2+2I_3+I_4=0$
Loop $AFBA$ or loop $ECDE$ :
$r{I}_1=r{I}_2+r{I}_3$
or $I_1=I_2+I_3$

Loop $BEFB$ or loop $EDFE$ :
$r\left(I_2-I_3\right)+r{I}_4=r{I}_3\text{ or }{I}_2-2I_3+I_4=0$
Loop $AFDCMA$ or $ABECMA$ :
$V=r{I}_1+r\left(I_2-I_3\right)+r{I}_2=r{I}_1+2r{I}_2-r{I}_3$
Solve to get $I_1=2V/5r,I_2=V/3r$
$R_{eq}=\frac{V}{I}=\frac{V}{I_1+I_2}$
$=\frac{V}{2V/5r+V/3r}=\frac{15r}{11}$