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 isb.halved?

Open in App
Solution

## Step 1- Relationship between resistance and length of the conductorThe resistance $R$ is directly proportional to the length $l$ of the wire. $R=\frac{\rho l}{A}$Where $\rho$ 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 changedBefore the change in the length of the conductor, the above expression is reduced to ${R}_{1}=\frac{\rho {l}_{1}}{A}...\left(1\right)$Where ${R}_{1}$ is the resistance of the conductor before the change and ${l}_{1}$ is the initial length of the conductor.After the change in the length of the conductor, the above expression is reduced to ${R}_{2}=\frac{\rho {l}_{2}}{A}...\left(2\right)$Where ${R}_{2}$ is the resistance of the conductor after the change and ${l}_{2}$ is the final length of the conductor.Divide equation $\left(2\right)$ by equation $\left(1\right)$ to obtain the expression for ${R}_{2}$.$\frac{{R}_{2}}{{R}_{1}}=\frac{\frac{\rho {l}_{2}}{A}}{\frac{\rho {l}_{1}}{A}}\phantom{\rule{0ex}{0ex}}{R}_{2}={R}_{1}\left(\frac{{l}_{2}}{{l}_{1}}\right)...\left(3\right)$Step 3- (b) Finding the value of resistance after the length of wire is halvedHere, the length of a conductor is halved so, ${l}_{2}=\frac{1}{2}{l}_{1}$Substitute $\frac{1}{2}{l}_{1}$ for ${l}_{2}$ into eqiuation $\left(3\right)$.${R}_{2}={R}_{1}\left(\frac{\frac{1}{2}{l}_{1}}{{l}_{1}}\right)\phantom{\rule{0ex}{0ex}}{R}_{2}=\frac{1}{2}{R}_{1}$Hence, the resistance also gets halved when the length of a wire is halved.

Suggest Corrections
7
Join BYJU'S Learning Program
Related Videos
Electric Current
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program