A uniform wire of resistance R is cut into 6 equal segments. Three of these segments are connected in series to form a combination X . The remaining three segments are connected in parallel to form a combination Y . If

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Correct answer: A. (R)/(20)

Resistance of the uniform wire = R When cut into 6 equal segments, the resistance of each segment is r = (R)/(6) Combination X consists of 3 segments in series. Resistance of X , R_X = 3r = 3 × (R)/(6) = (R)/(2) Combination Y consists of 3 segments in parallel. Resistance of Y , R_Y = (r)/(3) = (1)/(3) × (R)/(6) = (R)/(18) Combinations X and Y are connected in parallel. The equivalent resistance R_ eq is given by: 1 R_ eq = (1)/(R_X) + (1)/(R_Y) 1 R_ eq = (2)/(R) + (18)/(R) = (20)/(R) R_ eq = (R)/(20) Answer: (R)/(20)

A uniform wire of resistance R is cut into 6 equal segments. Three...

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