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

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:

$\displaystyle \frac{1}{R_e}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}$

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:

$\displaystyle \frac{1}{R_e}=\frac{1}{R/10}+\frac{1}{R/10}+\frac{1}{R/10}+...+\frac{1}{R/10}$

Note the sum consists of 10 equal terms. Operating on each term:

$\displaystyle \frac{1}{R_e}=\frac{10}{R}+\frac{10}{R}+\frac{10}{R}+...+\frac{10}{R}$

The sum of 10 identical fractions yields 10 times each fraction:

$\displaystyle \frac{1}{R_e}=10\frac{10}{R}=\frac{100}{R}$

Solving for Re needs to take the reciprocal of both sides of the equation:

$R_e=R/100$

The equivalent resistance of the combination is R/100