Question

A copper wire of length Land cross sectional area Ais used in an electrical application. If the same wire is cut in half and the two pieces are connected in parallel in the same application, how does the wire resistance in the latter connection compare to the wire resistance in the initial connection

Answer 1

Answer:

Explanation:

Given

Length of wire is  L

Area of cross-section is A

Resistance of wire is given by

$R=\frac{\rho L}{A}$

where $\rho =resistivity$

if wire is cut into two halves of equal length then

$L'=0.5 L$

New resistance of each piece

$R'=\frac{\rho \cdot 0.5L}{A}$

$R'=0.5 R$

if they are connected in parallel then net resistance is given by

$R'_{parallel}=\frac{R'\times R'}{R'+R'}$

$R'_{parallel}=\frac{R'}{2}$

$R'_{parallel}=\frac{R}{4}$

Thus Net resistance of new connection is $\frac{1}{4}$ th of the previous one