Current Electricity Ques 35
35. 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: 35.(c)
Solution:
- (c) Resistance is directly proportional to length and inversely proportional to cross-sectional area.
$\frac{1}{R _{A B}}=\frac{1}{3}+\frac{1}{4+5}=\frac{1}{3}+\frac{1}{9}=\frac{4}{9}$
$R _{A B}=\frac{3 \times(4+5)}{3+(4+5)}=\frac{27}{12}$
Similarly,
$R _{B C}=\frac{4 \times(3+5)}{4+(3+5)}=\frac{32}{12}$
$R _{A C}=\frac{5 \times(3+4)}{5+(3+4)}=\frac{35}{7}$
$\therefore R _{A B}: R _{B C}: R _{A C}=27: 32: 35$
BETA
