A letter \('A'\) is constructed of 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 \(60\) . The resistance between the ends of the legs is close to ................ \(\Omega\)

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(D) \(26.7\)

Detailed explanation

For \(ADE\) \(\frac{1}{\mathrm{R}^{\prime}}=\frac{1}{2 \mathrm{x}}+\frac{1}{10}\)

or \(\quad \mathrm{R}^{\prime}=\frac{20 \mathrm{x}}{10+2 \mathrm{x}}\)

\(\mathrm{R}_{\mathrm{BC}}=\frac{20 \mathrm{x}}{10+2 \mathrm{x}}+20-\mathrm{x}+20-\mathrm{x}\) ....\((i)\)

or \(\frac{20 x}{10+2 x}+40=2 x\)

Solving we get

\(x=10\, \Omega\)

Putting the value of \(x=10\, \Omega\) in equation \(( i )\) We get

\( R_{B C} =\frac{20 \times 10}{10+2 \times 10}+20-10+20-10 \)

\(=\frac{80}{3}=26.7\, \Omega \)

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