Question

A letter ' $A$ ' is constructed from 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 $60^{\circ} .$ The resistance between the ends of the legs is

• A. $50.0\, \Omega$
• B. $26.7\, \Omega$
• C. $2.72\, \Omega$
• D. $34.0\, \Omega$

Answer 1

Answer: (B)

A letter ' $A$ ' with its sides is as shown in the figure.
$D$ and $E$ are the mid points of the sides $F G$ and $F H$ respectively.
Resistance of side $D F$ is $=1\, \Omega cm ^{-1} \times 10\, cm =10\, \Omega$
Similarly, the resistance of other sides can be calculated and is as shown in the figure. Resistance between $D$ and $E$ is
$=\frac{20 \times 10}{20+10}=\frac{20}{3}\, \Omega$
The resistance between the ends of legs of letter ' $A'$ (i.e., between points $G$ and $H$ ) is
$=10\, \Omega+\frac{20}{3}\, \Omega+10\, \Omega=\frac{80}{3}\, \Omega=26.7\, \Omega$