A) 6 : 3 : 2
B) 1 : 2 : 3
C) 5 : 4 : 3
D) 4 : 3 : 2
Correct Answer: C
Solution :
Resistance between points A and B \[{{R}_{AB}}=r|\,|\left( \frac{r}{3}+\frac{r}{2} \right)\] \[=\frac{r\times 5/6\,\,r}{r+5/6r}=\frac{5}{11}r\] 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 \[{{R}_{CA}}=\frac{r}{3}|\,|\left( \frac{r}{2}+r \right)\] \[=\frac{\left( \frac{r}{3}\times \frac{3r}{2} \right)}{\frac{r}{3}+\frac{3r}{2}}\] \[=\frac{3}{11}r\] \[{{R}_{AB}}:{{R}_{BC}}:{{R}_{CA}}=5:4:3\]You need to login to perform this action.
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