Question

A letter A is constructed of a uniform wire of resistance $1\Omega /cm$. The sides of the letter are $20cm$ and the cross piece in the middle is $10cm$ long.The resistance between the ends of the legs will be:

• A. $32.4\Omega$
• B. $28.7\Omega$
• C. $26.7\Omega$
• D. $24.7\Omega$

Answer 1

The correct option is C $26.7\Omega$

The upper two resistances above the middle branch are in series. Thus their equivalent resistance is $20\Omega$. This $20\Omega$ resistance and the $10\Omega$ resistance of the middle branch are in parallel. Thus their equivalent resistance $\left(x\right)$ is given as $\frac{1}{20}+\frac{1}{10}=\frac{1}{x}$
or
$x=\frac{20}{3}ohms$
Now this $x$ and the remaining two resistances of $10\Omega$ each are in series. Thus we get the total equivalent resistance as:

$10+10+\frac{20}{3}=\frac{80}{3}=26.7\Omega$