Question

NA 110 A wire is cut into three equal parts and then connected in parallel with the same source. How
will its
(i) resistance and resistivity gets affected ?
(ii) How would the total current and the current through the parts change ?
(C.B.S.E.)

Answer 1

Given:

A wire is cut into three equal parts and then connected in parallel with the same source.

To find:

• How resistance and resistivity gets affected?
• What is the new current?

Calculation:

• Since resistivity is a materialistic property, it will still remain the same irrespective of the dimensions of the wire.

For constant area, resistance varies with length as:

$\boxed{R \propto l}$

• So, when wire is cut into 3 parts, length becomes l/3. Hence, resistance of each part is R/3.

• Now, when three R/3 parts are put in parallel, net resistance becomes (R/3)/3 = R/9.

Now, new current becomes :

$i_{new} = \dfrac{voltage}{new \: resistance}$

$\implies i_{new} = \dfrac{voltage}{R/9}$

$\implies i_{new} = 9 \times \dfrac{voltage}{R}$

$\implies i_{new} = 9 i$

So, current becomes 9 times the initial current.