A $12 Ω$ resistance is cut into three equal parts and then connected in triangular form. Determine the equivalent resistance between two ends of any side of the triangle.

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Solution

Resistance being proportional to length of wire, as the wire (object) is cut into three equal parts, then resistance of each part = $\frac{12}{3} = 4 Ω$
These parts are joined to form equilateral triangle.
Two resistances will be in series and their equivalent resistance will be parallel with resistance of third side.
Equivalent resistance, $R =$ $\frac{(4 + 4) \times 4}{(4 + 4) + 4} = \frac{8}{3} Ω$

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A 12Ω resistance is cut into three equal parts and then connected in triangular form. Determine the equivalent resistance between two ends of any side of the triangle.

A $12 Ω$ resistance is cut into three equal parts and then connected in triangular form. Determine the equivalent resistance between two ends of any side of the triangle.