A) 3 : 4 : 5
B) 9 : 16 : 25
C) 27 : 32 : 35
D) 21 : 24 : 25
Correct Answer: C
Solution :
[c] Resistance is directly proportional to length \[\frac{1}{{{R}_{AB}}}=\frac{1}{3}+\frac{1}{4+5}=\frac{\left( 4+5 \right)+3}{\left( 3 \right)\left( 4+5 \right)}\] \[{{R}_{AB}}=\frac{3\times \left( 4+5 \right)}{3+\left( 4+5 \right)}=\frac{27}{12}\] Similarly, \[{{R}_{BC}}=\frac{4\times \left( 3+5 \right)}{4+\left( 3+5 \right)}=\frac{32}{12}\] \[{{R}_{AC}}=\frac{5\times \left( 3+4 \right)}{5+\left( 3+4 \right)}=\frac{35}{12}\] \[\therefore {{R}_{AB}}:{{R}_{BC}}:{{R}_{AC}}=27:32:35\]
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