Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l/2 then the resistance of this wire will be

examrobotsa's picture
Q: 30 (NDA-I/2019)
Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l/2 then the resistance of this wire will be

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,3,5,0,2,3,3

When comparing the resistance of two wires, we can use the formula

R = (ρ * L) / A

where R is the resistance, ρ is the resistivity of the wire (which is constant for a given material such as copper), L is the length of the wire, and A is the cross-sectional area of the wire.

In this question, we are comparing two copper wires. The first wire has a radius of r and a length of l, and the second wire has a radius of 2r and a length of l/2.

To compare the resistance of the two wires, we need to calculate the cross-sectional area of each wire and then plug those values into the resistance formula.

The cross-sectional area of a wire is given by the formula A = π * r^2, where r is the radius of the wire.

For the first wire, the cross-sectional area is A1 = π * r^2.

For the second wire, the cross-sectional area is A2 = π * (2r)^2 = 4π * r^2.

Plugging these values into the resistance formula, we get:

R1 = (ρ * l) / A1

R2 = (ρ * (l/2))