Question

A wire of length 10m and resistance 10 OHMS is cut into 10 equal parts. These parts are now connected in parallel, then the equivalent resistance of combination is :

(a) 10 OHMS
(b) 1/10 OHMS
(c) 1 OHM
(d) None of these​

Answer 1

Answer:

its true answer is 1 ohm

Answer 2

The equivalent resistance of combination is $\dfrac{1}{10}\ \Omega$.

Explanation:

Length of wire is 10 m and resistance 10 ohms is cut into 10 equal parts. These parts are now connected in parallel, then the resistance of each part becomes r ohms, r=R/10

We need to find the equivalent resistance of combination.

For parallel combination, the equivalent resistance is given by :

$\dfrac{1}{r_{eq}}=\dfrac{1}{r_1}+\dfrac{1}{r_2}+.....\dfrac{1}{r_{10}}\\\\\dfrac{1}{r_{eq}}=\dfrac{1}{r}+\dfrac{1}{r}+.....\text{10 times }\\\\\dfrac{1}{r_{eq}}=\dfrac{10}{r}\\\\\dfrac{1}{r_{eq}}=\dfrac{10}{(R/10)}\\\\{r_{eq}=\dfrac{R}{100}$

We have R = 10 ohms

So,

${r_{eq}=\dfrac{10}{100}\\r_{eq}=\dfrac{1}{10}\ \Omega$

So, the equivalent resistance of combination is $\dfrac{1}{10}\ \Omega$.

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