A uniform wire is cut 10 segments increasing in length in equal steps. The resistance of shortest segment is R and the resistance of the other segments increases in steps of `4 Omega`. If the resistance of the longest segment is 2R, find the value of R and the resistance of original wire.
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Resistance of first segment `= R Omega` Resistance of second segment = `R + 4 xx 1 Omega` Resistance of third segment `=R + 4 xx 2 Omega` Resistance of tenth segment `= R + 4 xx 9` `= R + 36 Omega` As per question, `R + 36 = 2R or R = 36 Omega` Resistance of the origin wire `R + (R +4) + (R + 8) +(R + 12) +...` `+ (R + 36)` `10R +4(1+2+3+...+9)` `=10 xx 36+4 xx 45 = 540 Omega`
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