CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Two copper wire A and B of length 30m and 10m have radii 2cm and 1cm respectively. Compare the resistance of the two wires. Which will have less resistance?

Open in App
Solution

Step 1: Given that:

Length of copper wire A (lA) = 30m

Radius of wire A (rA) = 2cm=2×102m

length of copper wire B(lB) = 10m

Radius of copper wire B(rB) = 1cm=102m

Step 2: Comparison of the resistances of both wires A and B:

The resistivity of a conductor is given by;

R=ρlA

ρ=RAl

Where R is the resistance of the conductor, l is the length and A is the area of the cross-section of the conductor.

Since both wires, A and B are made of copper, their resistivity will be the same.

ρA=ρB

RAAAlA=RBABlB

Putting the given values we get;

RA×π×(2×102m)230m=RB×π×(102m)210m

RARB=3010×4

RARB=34

Step 3: Determination of the maximum resistance between A and B:

Since; RARB=34

Thus,

RA=RB34

RB=43RA

RB=1.11RA

That is;

RB>RA

Thus, wire B has the maximum resistance.

Thus,
RARB=34
And, wire B has the maximum resistance.

flag
Suggest Corrections
thumbs-up
29
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Extraction of Metals and Non-Metals
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon