Question

A piece of metallic wire of resistance R is cut into 3 equal parts. These parts are then connected in parallel. If the total resistance of this combination is r , then the value of R : r is

Answer 1

Answer:

1:9

Explanation:

each resistance=R/3

In parallel,1/r=3/R+3/R+3/R

1/r=9/R

∴R:r=1:9

Answer 2

Concept Introduction: Resistance is given by Potential difference divided by per unit Current.

Given:

We have been Given: Resistance is given as R

Cut into 3 equal parts. Total Resistance is r .

To Find:

We have to Find: Find R:r

Solution:

According to the problem, Resistance is R , cut into 3 equal parts, therefore resistance of 3 parts are

$\frac{r}{3}$

they are connected in parallel, so,

$\frac{1}{r} (total) = \frac{3}{r} + \frac{3}{r} + \frac{3}{r} = \frac{9}{r}$

therefore,

$r(total) = \frac{r}{9}$

Therefore, R:r will be 1 : 9

Final Answer: R : r is 1 : 9

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