Question

A letter 'A' is constructed of a uniform wire of resistance $1ohm/cm$. The sides of the letter are $20cm$ long and the cross piece in the middle is $10cm$ long while the vertex angle is ${60}^o$. The resistance of the letter between the two ends of the legs is:

• A. $\frac{40}{3}\Omega$
• B. $\frac{80}{3}\Omega$
• C. $40\Omega$
• D. $10\Omega$

Answer 1

The correct option is B $\frac{80}{3}\Omega$

Equivalent circuit is shown above.

Effective resistance between C and D $R_{CD}=(10+10)\parallel 10=20\parallel 10=\frac{20\times 10}{20+10}=\frac{20}{3}\Omega$

$\therefore$ Equivalent resistance between A and B $R_{AB}=10+R_{CD}+10=\frac{80}{3}\Omega$