As the length of a wire increases the resistance

Asked by admin @ 23/08/2021 in Physics viewed by 319 People

If the length of wire increases by 1/3 times then its resistance becomes

Answered by admin @ 23/08/2021

Answer- The above question is from the chapter 'Electricity'.

Let's know about resistance.

Resistance- It is the property of a conductor, semi-conductor or insulator to resist the flow of charges.

R = V/I

where R = Potential difference between two end points and I = flow of current.

Resistance is generally measured in Ohms. (Ω)

R = $\frac{\rho l}{A}$

where ρ = resistivity, l = length of material and A = area of material.

R ∝ l

R ∝ ρ

R ∝ 1/A

Given question: If the length of wire increases by 1/3 times, then its resistance becomes ____________.

Solution: Let R be the resistance of the given wire, ρ be its resistivity, l be its length and A be its area.

We know that R = $\frac{\rho l}{A}$

Original resistance (R) = $\frac{\rho l}{A}$

When the length of wire increases by 1/3 times, its area decreases by 3 times.

New resistance (R') = $\frac{\rho *1l}{3 * 3A}$

= $\frac{\rho l}{9A}$

= $1/9 \frac{\rho l}{A}$

So, the new resistance 1/9 times the original resistance.

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