Question

A piece of copper wire is cut into 10
equal parts, thise part are connected in parallel.
the joint resistance of parallal combination
will be equal to the orignal distance of
uncut wire. multiplied the factor of
​

Answer 1

Given:

A piece of copper wire is cut into 10 equal parts .

these parts are connected in parallel combination

To Find:

Resistance of the combination

Solution:

Resistance is defined as a property of body to obstruct the flow of current.

Resistance in series

$R_{eq} = R_{1} + R_{2}$

Resistance in parallel

$\frac{1}{R_{eq} } = \frac{1}{R_{1} } + \frac{1}{R_{2} }$

Resistance is directly proportional to length and inversely proportional to area.

   $R \alpha L$

Let the length of wire is L

length of 10 equal parts = $\frac{L}{10}$

R of each wire is equal to $\frac{R}{10}$

Equivalent resistance

$\frac{1}{R_{eq} }= \frac{1}{R_{1} } + \frac{1}{R_{2} } .................... \frac{1} {R_{10} }$

$R_{1} = R_{2}= R_{3} ........................ R_{10} = \frac{R}{10}$

$\frac{1}{R_{eq} } = 10(\frac{10}{R}) \\\\R_{eq} = \frac{R}{100}$

The joint resistance of parallel combination will be equal to the original distance multiplied by a factor of $\frac{1}{100}$ .