Two cylindrical copper wires have the same mass and are at the same temperature. Wire A is twice as long as wire B. The resistance of wire A is related to that of wire B by :
a) RA = RB/4
b) RA = RB/2
c) RA = RB
d) RA = 2RB
e) RA = 4RB
To determine the relationship between the resistance of wire A (RA) and wire B (RB), we need to use the formula for resistance:
Resistance (R) = (resistivity * length) / area
Since both wires have the same mass and are at the same temperature, we can assume that their resistivity and cross-sectional area are the same. Therefore, the only difference between the two wires is their length.
Given that wire A is twice as long as wire B, we can express the relationship of the lengths as follows:
Length of wire A = 2 * Length of wire B
Using this relationship, we can substitute the values back into the resistance formula:
RA = (resistivity * length of wire A) / area
= (resistivity * 2 * length of wire B) / area
= 2 * (resistivity * length of wire B) / area
= 2 * RB
Therefore, the relationship between the resistance of wire A (RA) and wire B (RB) is:
RA = 2RB
So, the correct option is d) RA = 2RB.