A piece of wire of resistance r is cut into 5 equal pieces. These parts are then connected in parallel. If the equivalen resistance of this combination is R' .then the ratio R/R' is
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When a wire of resistance R is cut into five equal parts then the resistance of each part will be r/5 because resistance is directly proportional to the length of wire.
When these parts are connected in parallel combination then their equivalent resistance becomes
1/R'=1/R1+1/R2+1/R3+1/R4+1/R5
1/R'=5/R+5/R+5/R+5/R+5/R
1/R'=5+5+5+5+5/R
1/R'=25/R
R'=R/25
Ratio=R/R'=25R/R
=25:1
When these parts are connected in parallel combination then their equivalent resistance becomes
1/R'=1/R1+1/R2+1/R3+1/R4+1/R5
1/R'=5/R+5/R+5/R+5/R+5/R
1/R'=5+5+5+5+5/R
1/R'=25/R
R'=R/25
Ratio=R/R'=25R/R
=25:1
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