Question

For the circuit shown in Fig. 5.297, 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

The correct option is D $\frac{15}{11}r$

From the above figure,

At junction $E$ or $F$:

$I_1+I_3+I_4=I_2-I_3\Rightarrow I_1-I_2+2I_3+I_4=0$

Loop $AFBA$ or loop $ECDE$

$r{I}_1=r{I}_2+r{I}_3\Rightarrow I_1=I_2+I_3$

Loop $BEFB$ or loop $EDFE$:

$r(I_2-I_3)+r{I}_4=r_3\Rightarrow I_2-2I_3+I_4=0$

Loop $AFDCMA$ or $ABECMA$

$V=r{I}_1+r(I_2-I_3)+r{I}_2\Rightarrow V=r{I}_1+2r{I}_2-I{r}_3$

Solve to get $I_1=2V/5r,I_2=V/3r$

$R_{eq}=\frac{V}{I}=\frac{V}{I_1+I_2}=\frac{V}{2V/5r+V/3r}=\frac{15r}{11}$