A piece of wire having a resistance R is cut into five equal parts.
(1) How will the resistance of each part of the wire compare with the original resistance?
(i) If the five parts of the wire are placed in parallel, how will the resistance of the combination
compare with the resistance of the original wire? What will be ratio of resistance in series to
that of parallel?
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Resistance of a piece of wire is proportional to its length. A piece of wire has a resistance R. The wire is cut into five equal parts.
➧ Therefore, resistance of each part
➾ R/5
➧ All the five parts are connected in parallel.
∴equivalent resistance (R') is given as
1 / R'
➾ 5 / R + 5 / R + 5 / R + 5 / R + 5
➾ 5 + 5 + 5 + 5 + 5 / R
➾ 1 / R' = 25 / R
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