Question

A letter ' $A$ ' is constructed from 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 $60^{\circ }.$ 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 $FG$ and $FH$ respectively.
Resistance of side $DF$ is $=1\Omega c{m}^{-1}\times 10cm=10\Omega$
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 ' $A^{\prime }$ (i.e., between points $G$ and $H$ ) is
$=10\Omega +\frac{20}{3}\Omega +10\Omega =\frac{80}{3}\Omega =26.7\Omega$