Question

in how many equal parts a wire of resistance 100 ohm be cut so as to get an effective resistance of 10 ohm is obtained by connecting them in parallel

Answer 1

it means the resistance is being measured as series resistance. Since the resistance of a conductor, considering the cross sectional area, is proportional to its length,

we chose 10 equal parts because the wires will be connected in parallel after being cut.

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

there fore 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