Question

What what is the number of equal part into which the conductor having resistance r =100 ohm should be cut to obtain the resistance r1 =1ohm if parts are connected in parallel

Answer 1

When two resistors of same resistance are connected parallel to each other then the resultant is half of the original resistance.

Thus, if the total resistance of a wire is 100 ohm it means that the resistance is being measured as a series resistance. Since the resistance of a conductor, considering the cross sectional area, is proportional to its length,  we will choose 10 equal parts as the wires will be connected in parallel after they are cut.  Hence equivalent resistance will be given by R-

Resistors in parallel is 1/RT = 1/R1 + 1/R2 + 1/R3 … 1/R10

= 1/RT = 1/10 + 1/10 + 1/10 … 1/10  or 1/10 x 10

=1/RT = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1

1/RT = 1

RT = 1