CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

What is the effect of the length on the resistance of a conductor? How does the resistance of a wire change when its length is

b.halved?


Open in App
Solution

Step 1- Relationship between resistance and length of the conductor

The resistance R is directly proportional to the length l of the wire.

R=ρlA

Where ρ is the resistivity and A is the cross-section area of the wire,

Hence, the resistance of a conductor increases with an increase in length, and the resistance of a conductor decreases with a decrease in length.

Step 2- Finding the formula for the resistance after the length of the conductor is changed

Before the change in the length of the conductor, the above expression is reduced to

R1=ρl1A...(1)

Where R1 is the resistance of the conductor before the change and l1 is the initial length of the conductor.

After the change in the length of the conductor, the above expression is reduced to

R2=ρl2A...(2)

Where R2 is the resistance of the conductor after the change and l2 is the final length of the conductor.

Divide equation (2) by equation (1) to obtain the expression for R2.

R2R1=ρl2Aρl1AR2=R1l2l1...(3)

Step 3- (b) Finding the value of resistance after the length of wire is halved

Here, the length of a conductor is halved so, l2=12l1

Substitute 12l1 for l2 into eqiuation (3).

R2=R112l1l1R2=12R1

Hence, the resistance also gets halved when the length of a wire is halved.


flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Electric Current
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon