A wire of resistance 20 Ohm is bent to form a closed square . What is the resistance across a diagonal of the square?

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Solution

Since the wire is bend in form of the square and we know that sides of square are equal so each side will have same resistance i.e 5 ohm. Now if we make diagonal two faces in each side of the diagonal will have two sides and resistance will be 10 ohm. As shown below:
If the wire is bent to form a square,then the resistance of each side of the square $= \frac{20}{4} = 5 o h m$

first calculate the resistance through the two sides that is
$R_{1} = 5 + 5 = 10 o h m$
$R_{2} = 5 + 5 = 10 o h m$

$R_{1} a n d R_{2}$ are in parallel

$\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$
$\frac{1}{R} = \frac{1}{10} + \frac{1}{10} = \frac{1 + 1}{10} = \frac{2}{10}$
$R = 5 o h m$

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