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A piece of wire of resistance R is cut into 5 equal parts . these are then connected in parallel to form a combination R1 . what will be the ratio of R1/R



If a resistance cut into n equal part then resistance of one resistor is = R/n
hence ,
resistance of all 5 resistor = R/5
all connected in parallel hence equivalent resistance 1/R1 = 1/R/5 + `1/R/5 + 1/R/5 + 1/R/5 + 1/R/5
1/R1 = 25/R
R/R1 = 25 
2 5 2

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Wire is cut into 5 equal parts. Since all dimensions are same for pieces, Resistance of each wire is equal and has a value = R/5.

Resistance is proportional to length of wire and inversely proportional to area of cross-section. IF length is 1/5th, then Resistance is also 1/5 th of original value.

When these five are connected in parallel combination, then net resistance becomes 1/5th again. So R1 = R/5 * 1/5 = R/25

Ratio = R1/R = 1/25

1 5 1
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