Question

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

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

Answer 1

The correct option is D $3\Omega$

When a metallic wire of resistance 12Ω12Ω is bent to form a square, the equivalent circuit diagram is as shown in the figure.
Resistance of arm ABC=3Ω+3Ω=6ΩABC=3Ω+3Ω=6Ω will be parallel to resistance of arm ADC=3Ω+3Ω=6ΩADC=3Ω+3Ω=6Ω
Their effective resistance is
=6Ω×6Ω6Ω+6Ω=3Ω=6Ω×6Ω6Ω+6Ω=3Ω
Hence, the resistance between diagonal points
i.e., between AA and CC is 3Ω