A letter'A' is constructed of a uniform wire with resistance $1.0 \Omega$ per $\mathrm{cm}$, The sides of the letter are $20 \mathrm{~cm}$ and the cross piece in the middle is 10 $\mathrm{cm}$ 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

  $36.7 \Omega$
• Correct answer
  D

  $26.7 \Omega$

Solution

For ADE $\frac{1}{R^{\prime}}=\frac{1}{2 x}+\frac{1}{10} \quad$ or $\quad R^{\prime}=\frac{20 x}{10+2 x}$ $\mathrm{R}_{\mathrm{BC}}=\frac{20 \mathrm{x}}{10+2 \mathrm{x}}+20-\mathrm{x}+20-\mathrm{x} \quad \ldots$(i) or $\quad \frac{20 \mathrm{x}}{10+2 \mathrm{x}}+40=2 \mathrm{x}$ Solving we get $\mathrm{x}=10 \Omega$ Putting the value of $x=10 \Omega$ in equation (i) We get $\mathrm{R}_{\mathrm{BC}}=\frac{20 \times 10}{10+2 \times 10}+20-10+20-10$ $=\frac{80}{3}=26.7 \Omega$

Hence, the correct answer is option: 'D'.