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

$R_0 = \frac{rL_0}{A_0}$

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:

$L =\frac{L_0}{3}$

$A=\frac{A_0}{3}$

Therefore the new resistance will be :

$R =R_0$

$R =\frac{rL}{A}$

$R =\frac{rL_0/3}{A_0/3}$

$R = \frac{1}{9} r\frac{L_0}{A_0}$

$R = \frac{1}{9} R_0$

$R = \frac{1}{9}* 11.9$

$R = 1.32\Omega$

Therefore the resistance of this new wire would be 1.32Ω