Question

A metal wire of resistance R is cut into two pieces of equal length. The two pieces are connected together side by side. Part A What is the resistance of the two connected wires?

Answer 1

When a wire of resistance R is cut into two equal pieces and connected side by side, the resistances of the two connected wires will be half of the original resistance.

Step-by-step explanation:

The resistance of a wire is determined by its length, cross-sectional area, and resistivity. In this case, when a wire of resistance R is cut into two equal pieces and connected side by side, the resistances of the two connected wires will be half of the original resistance.

This is because, when the wire is cut into two equal pieces, both pieces will have half of the original length, but the cross-sectional area and resistivity will remain the same. Since resistance is directly proportional to length, the resistance of each wire will be half of the original resistance (0.5R + 0.5R = R).

Therefore, the resistance of the two connected wires will be R/2.

Answer 2

R/2

Step-by-step explanation:

Resistance of full lenght wire = R

Since length is divided into half but even then the resistance of each individual half is same i-e R

If connecetd into parallel mode then we know resultant resistance say 'r' is

1/r=1/R+1/R

or

1/r = 2/R

r= R/2