A wire of uniform cross -section and length l  has a resistance of 4ohm . The wire is cut into 4 equal pieces. Each piece is then stretched to length 'l'.Thereafter the 4 wires are joined in parallel. Calculate the net resistance.

Asked by mkvinvestments6 | 20th Jul, 2015, 09:30: PM

Expert Answer:

Resistance of a material depends upon the nature of material, length of the wire and the area of cross section.
Let the resistivity of the material be begin mathsize 14px style straight rho end style,length of the wire be l and the area of cross section be A.
begin mathsize 14px style straight R equals straight rho 1 over straight A equals 4 straight capital omega end style
Now the wire is cut into four equal pieces and stretched to the initial length l.
When we stretch it the new length of the wire will be the same of each piece but the area will get reduced to one-fourth.
l'=l
begin mathsize 14px style straight A apostrophe equals straight A over 4 therefore Resistance space of space each space piece comma space straight R apostrophe equals straight rho fraction numerator straight l apostrophe over denominator straight A apostrophe end fraction straight R apostrophe equals straight rho fraction numerator straight l over denominator left parenthesis straight A divided by 4 right parenthesis end fraction equals 4 straight rho straight l over straight A equals 4 straight R end style
Now connect the four pieces in parallel, the equivalent resistance will be,
begin mathsize 14px style straight R subscript straight p equals fraction numerator straight R apostrophe over denominator 4 end fraction equals fraction numerator 4 straight R over denominator 4 end fraction equals straight R equals 4 straight capital omega end style
Thus, the net resistance will be the same.

Answered by Faiza Lambe | 21st Jul, 2015, 08:04: AM