Q. A letter ' $A$ ' is constructed of a uniform wire with resistance $1.0\, \Omega$ per $cm$, The sides of the letter are $20\, cm$ and the cross piece in the middle is $10 \,cm$ long. The apex angle is $60$ . The resistance between the ends of the legs is close to:
BITSATBITSAT 2012
Solution:
The circuits are shown above.
Using trignometry, $\frac{5}{ x }=\sin 30=0.5$
$\Rightarrow x =10\, cm$
Thus we get $A B=C D=20-10=10\, cm$
Since all parts are of same length, thus resistance of each part
$R=10 \times 1=10 \,\Omega$
Equivalent circuit is also shown above.
Equivalence resistance between $B$ and $E$,
$R _{ BE }=(10+10)\|10=20\| 10$
$\therefore R_{ eq }=\frac{20 \times 10}{20+10}=6.7\, \Omega$
Equivalent resistance between $A$ and $D$,
$R _{ AD }=10+6.7+10=26.7\, \Omega$
