Question

A letter ' $A$ ' is constructed of a uniform wire with resistance $1.0\Omega$ per $cm$, The sides of the letter are $20cm$ and the cross piece in the middle is $10cm$ long. The apex angle is $60$ . The resistance between the ends of the legs is close to:

• A. $50.0\Omega$
• B. $10\Omega$
• C. $36.7\Omega$
• D. $26.7\Omega$

Answer 1

Answer: (D)

The circuits are shown above.
Using trignometry, $\frac{5}{x}=\sin 30=0.5$
$\Rightarrow x=10cm$
Thus we get $AB=CD=20-10=10cm$
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 $E$,
$R_{BE}=(10+10)\Vert 10=20\Vert 10$
$\therefore R_{eq}=\frac{20\times 10}{20+10}=6.7\Omega$
Equivalent resistance between $A$ and $D$,
$R_{AD}=10+6.7+10=26.7\Omega$