Current Electricity - Result Question 25

26. A $12 cm$ wire is given a shape of a right angled triangle $A B C$ having sides $3 cm, 4 cm$ and $5 cm$ as shown in the figure. The resistance between two ends $(A B, B C, C A)$ of the respective sides are measured one by one by a multi-meter. The resistances will be in the ratio of

[NEET Kar. 2013]

(a) $3: 4: 5$

(b) $9: 16: 25$

(c) $27: 32: 35$

(d) $21: 24: 25$

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Answer:

Correct Answer: 26. (c)

Solution:

  1. (c) Resistance is directly proportional to length,

$\frac{1}{R _{A B}}=\frac{1}{3}+\frac{1}{4+5}=\frac{(4+5)+3}{(3)(4+5)}$

$R _{A B}=\frac{3 \times(4+5)}{3+(4+5)}=\frac{27}{12}$

Similarly,

$R _{B C}=\frac{4 \times(3+5)}{4+(3+5)}=\frac{32}{12}$

$R _{A C}=\frac{5 \times(3+4)}{5+(3+4)}=\frac{35}{12}$

$\therefore R _{A B}: R _{B C}: R _{A C}=27: 32: 35$