Question

A letter ${}^{\prime }{A}^{\prime }$ is constructed of a uniform wire with resistance $1.0\Omega c{m}^{-1}$. 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. $34\Omega$

Answer 1

Answer: (B)

$26.7\Omega$

The circuits are shown above.

Using trignometry, $\frac{5}{x}=\sin 30=0.5$

$⟹x=10cm$

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, $R_{BE}=(10+10)\parallel 10=20\parallel 10$

$\therefore$ $R_{eq}=\frac{20\times 10}{20+10}=6.7\Omega$

Equivalent resistance between A and D, $R_{AD}=10+6.7+10=26.7\Omega$