Question

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

• A. $12Î\copyright$
• B. $24Î\copyright$
• C. $6Î\copyright$
• D. $3Î\copyright$

Answer 1

Answer: (D)

When a metallic wire of resistance $12Î\copyright$ is bent to form a square, the equivalent circuit diagram is as shown in the figure.

Resistance of arm $ABC=3Î\copyright +3Î\copyright =6Î\copyright$
will be parallel to resistance of arm $ADC=3Î\copyright +3Î\copyright =6Î\copyright$.
Their effective resistance is $=\frac{6Î\copyright ×6Î\copyright }{6Î\copyright +6Î\copyright }=3Î\copyright$
Hence, the resistance between diagonal points i.e., between $A$ and $C$ is $3Î\copyright$.