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  4. A metallic wire of resistance 12 Ω is bent to form a square. The resistance between two diagonal points would be

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Q. A metallic wire of resistance $12\, \Omega$ is bent to form a square. The resistance between two diagonal points would be

Current Electricity

Solution:

When a metallic wire of resistance $12\, \Omega$ is bent to form a square, the equivalent circuit diagram is as shown in the figure.
image
Resistance of arm $A B C=3\, \Omega+3\, \Omega=6\, \Omega$
will be parallel to resistance of arm $A D C=3\, \Omega+3\, \Omega=6\, \Omega$.
Their effective resistance is $ = \frac{6\,\Omega \times 6\,\Omega}{6\,\Omega + 6\,\Omega} = 3\,\Omega$
Hence, the resistance between diagonal points i.e., between $A$ and $C$ is $3\, \Omega$.