Question

IN HOW MANY EQUAL PARTS a wire having a resistance of 100 ohm be cut , so that we may obtain a resistance of 1 ohm by connecting them in parallel

Answer 1

Let the number of equal parts be 'n'

so, the resistance of each part will be = 100/n ohms

now, we know that the equivalent resistance of connecting 'n' resistance each of value 100/n is 1 ohm. So,

1/R_eq = 1/R₁ + 1/R₂ + ..............+ 1/R_n

here,

R_eq = 1 ohm

R₁ = R₂ = R_n = (100/n) ohm

so,

1/1 = 1 / (100/n) + ............. + 1/ (100/n)

or

1 = n / ( 100/n) = n² / 100

thus, the wire should be cut into

n = 10 equal parts