A wire is cut into three equal parts and then connected in parallel with the same source. How will it
(i) resistance and resistivity gets affected?
(ii) How would the total current and the current through the parts change?

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Solution

resistance is directly proportional to the length of the wire

equal part will have equal resistance

$fraction numerator 1 over denominator R e f f end fraction equals 1 over R plus 1 over R plus 1 over R fraction numerator begin display style 1 end style over denominator begin display style R e f f end style end fraction equals 3 over R R e f f equals R over 3 space o h m s$

current is inversely proportional to the resistance

since there are equal resistances in parallel. Equal amount of current will flow through each part

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