Question

A wire of resistance R is cut into ten equal parts which are then connected in parallel. The equivalent resistance of the combination is

Answer 1

The equivalent resistance of the combination is R/100

Step-by-step explanation:

Electric Resistance

The electric resistance of a wire is directly proportional to its length. If a wire of resistance R is cut into 10 equal parts, then each part has a resistance of R/10.

Parallel connection of resistances: If R1, R2, R3,...., Rn are connected in parallel, the equivalent resistance is calculated as follows:

`\displaystyle (1)/(R_e)=(1)/(R_1)+(1)/(R_2)+(1)/(R_3)+...+(1)/(R_n)`

If we have 10 wires of resistance R/10 each and connect them in parallel, the equivalent resistance is:

`\displaystyle (1)/(R_e)=(1)/(R/10)+(1)/(R/10)+(1)/(R/10)...+(1)/(R/10)`

This sum is repeated 10 times. Operating each term:

`\displaystyle (1)/(R_e)=(10)/(R)+(10)/(R)+(10)/(R)+...+(10)/(R)`

All the terms have the same denominator, thus:

`\displaystyle (1)/(R_e)=10(10)/(R)=(100)/(R)`

Taking the reciprocals:

`R_e=R/100`

The equivalent resistance of the combination is R/100