A wire of uniform resistance λ Ω/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (AOB) as shown in figure. The equivalent resistance between points A and B i $s _____Ω.$

Question

G1 Physics · Accepted Answer

There are three independent conducting paths between A and B. 1. Short circular arc AB: The angle subtended is 90°, so its length is πr/2. Hence, R₁ = λπr/2. 2. Long circular arc AB: Its angle is 270°, so its length is 3πr/2. Hence, R₂ = 3λπr/2. 3. Straight bent path AOB: Its total length is 2r. Hence, R₃ = 2λr. These three resistances are in parallel. Therefore, 1/R = 1/R₁ + 1/R₂ + 1/R₃ = 2/(λπr) + 2/(3λπr) + 1/(2λr). Taking 1/(λr) common, 1/R = [2/π + 2/(3π) + 1/2]/(λr). Simplifying, 1/R = (1…

A wire of uniform resistance λ Ω/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (AOB) as shown in figure. The equivalent resistance between points A and B i s _____Ω.