Question

In how many parts (equal) a wire of 100 Ω be cut so that a resistance of 1 Ω is obtained by connecting them in parallel ?​

Answer 1

Answer:

10 equal

If the total resistance of a wire is 100 ohm 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.

Answer 2

Answer:

10 parts

Explanation:

Given :

• A wire of resistance 100 ohms is cut into equal parts
• The parts of wire are connected in parallel to obtain equivalent resistance of 1 ohm

To find :

• No. Of parts to be connected in parallel

When 10 resistors of equal resistance are connected in parallel:

$\frac{1}{req} = \frac{1}{r1} + \frac{1}{r2} ....... \frac{1}{r10}$

$\frac{1}{req} = \frac{1}{r} + \frac{1}{r} ..... \frac{1}{r}$

$req = \frac{10}{r}$

$req = \frac{r}{10}$

Here r = 100 ohms, Substituting the value, we get:

$parts= \frac{100}{10}$

$parts= 10 \:$

10 parts must be connected in parallel for the above condition