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