Question

Six resistances each of value $r=6\Omega$. are connected between points $A,B$ and $C$ as shown in the figure. If $R_1,R_2$ and $R_3$ are the net resistances between $A$ and $B$, between $B$ and $C$ and between $A$ and $C$ respectively, then $R_1:R_2:R_3$ will be equal to

• A. 6 : 3 : 2
• B. 1 : 2 : 3
• C. 5 : 4 : 3
• D. 4 : 3 : 2

Answer 1

Answer: (C)

Resistance between points $A$ and $B$
$R_{AB}=r\Vert \left(\frac{r}{3}+\frac{r}{2}\right)$
$=\frac{r\times 5/6r}{r+5/6r}=\frac{5}{11}r$
Resistance between points $B$ and $C$
$R_{BC}=\frac{r}{2}||\left(r+\frac{r}{3}\right)=\frac{\frac{r}{2}\times \frac{4r}{3}}{\frac{r}{2}+\frac{4r}{3}}=\frac{4}{11}r$
Resistance between points $C$ and $D$
$R_{CA}=\frac{r}{3}\Vert \left(\frac{r}{2}+r\right)=\frac{\left(\frac{r}{3}\times \frac{3r}{2}\right)}{\frac{r}{3}+\frac{3r}{2}}=\frac{3}{11}r$
$R_{AB}:R_{BC}:R_{CA}=5:4:3$