Answer:
The equivalent resistance of the combination is R/100
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:
[tex]\displaystyle \frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}[/tex]
If we have 10 wires of resistance R/10 each and connect them in parallel, the equivalent resistance is:
[tex]\displaystyle \frac{1}{R_e}=\frac{1}{R/10}+\frac{1}{R/10}+\frac{1}{R/10}...+\frac{1}{R/10}[/tex]
This sum is repeated 10 times. Operating each term:
[tex]\displaystyle \frac{1}{R_e}=\frac{10}{R}+\frac{10}{R}+\frac{10}{R}+...+\frac{10}{R}[/tex]
All the terms have the same denominator, thus:
[tex]\displaystyle \frac{1}{R_e}=10\frac{10}{R}=\frac{100}{R}[/tex]
Taking the reciprocals:
[tex]R_e=R/100[/tex]
The equivalent resistance of the combination is R/100
