Answer:
The equivalent resistance of the combination is R/100
Explanation:
Parallel Connection of Resistances
If resistances 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]
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.
It's known the 10 parts or resistance R/10 were connected in parallel, thus the electric 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]
Note the sum consists of 10 equal terms. Operating on each term:
[tex]\displaystyle \frac{1}{R_e}=\frac{10}{R}+\frac{10}{R}+\frac{10}{R}+...+\frac{10}{R}[/tex]
The sum of 10 identical fractions yields 10 times each fraction:
[tex]\displaystyle \frac{1}{R_e}=10\frac{10}{R}=\frac{100}{R}[/tex]
Solving for Re needs to take the reciprocal of both sides of the equation:
[tex]R_e=R/100[/tex]
The equivalent resistance of the combination is R/100
