Question

An 11.9 Ω metal wire is cut into three equal pieces which are then connected side by side to form a new wire (with length one-third the original length). What is the resistance of this new wire? Answer in units of Ω

Answer 1

We will use the concepts defined for the calculation of resistance from resistivity, length and area. Mathematically this is defined as

`R_0 = (rL_0)/(A_0)`

Where,

r = Resistivity

`L_0`= Length of wire

`A_0`= Cross sectional Area

`R_0 = 11.9\Omega \Rightarrow` the Resistance given.

As there was a cut of three pieces, and equal parts are added over them the length and final area will be:

`L =(L_0)/(3)`

`A=(A_0)/(3)`

Therefore the new resistance will be :

`R =R_0`

`R =(rL)/(A)`

`R =(rL_0/3)/(A_0/3)`

`R = (1)/(9) r(L_0)/(A_0)`

`R = (1)/(9) R_0`

`R = (1)/(9)* 11.9`

`R = 1.32\Omega`

Therefore the resistance of this new wire would be 1.32Ω