Circular Resistance?

Electricity and Magnetism Level 2

A wire of resistance 12 Ω / m 12\ \Omega/m is bent to form a complete circle of radius 10 cm \text{10 cm} as shown in the figure. What is the resistance between its two diametrically opposite points A A and B B ?

6 Ω 6\ Ω 6 π Ω 6 π\ Ω 3 Ω 3\ Ω 0.6 π Ω 0.6 π\ Ω

Aditya Shrivastava by Aditya Shrivastava , 17, India

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1 solution

Max Yuen
Jun 3, 2019

The total resistance of the ring is R = ( 12 Ω / m ) × 2 π ( 0.1 m ) = 2.4 π Ω R=(12\Omega/m )\times 2\pi(0.1m) = 2.4\pi\Omega .

When the resistance is measured diametrically, it is equivalent to having the total resistance cut into two equal resistors with resistance equal to R / 2 R/2 but placed in parallel. Thus, the parallel resistance is equivalent to ( 1 R / 2 + 1 R / 2 ) − 1 = R / 4 = 0.6 π Ω \left(\frac{1}{R/2}+\frac{1}{R/2}\right)^{-1}=R/4 = 0.6\pi\Omega .

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Can you please elaborate

Aditya Shrivastava - 2 years ago

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