How does the resistance of a wire change when: 1. Its length is tripled? 2. Its diameter is tripled? 3. Its material is changed to one whose resistivity is three times?

R= I A 1. I → 3I R'= 3I A =3R Resistance gets tripled. 2. d → 3d R= I A =R= I ^2 = I ( d 2 )^2 R'= I ( 3d 2 )^2 =1 9 I ( d 2 )^2 = R 9 Resistance becomes 1 9 th. 3. R= I A 3 R'=3 I A =3R Resistance becomes 3 times.

How does the resistance of a wire change when: 1. Its length is t…

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Question

How does the resistance of a wire change when:

Its length is tripled?
Its diameter is tripled?
Its material is changed to one whose resistivity is three times?

✓

Answer

$\text{R}=\rho\frac{\text{I}}{\text{A}}$

I → 3I

$\text{R}'=\rho\frac{3\text{I}}{\text{A}}=3\text{R}$

Resistance gets tripled.

d → 3d

$\text{R}=\rho\frac{\text{I}}{\text{A}}=\text{R}=\rho\frac{\text{I}}{\pi\text{r}^2}=\rho\frac{\text{I}}{\pi\big(\frac{\text{d}}{2}\big)^2}$

$\text{R}'=\rho\frac{\text{I}}{\pi\big(\frac{3\text{d}}{2}\big)^2}=\frac{1}{9}\rho\frac{\text{I}}{\pi\big(\frac{\text{d}}{2}\big)^2}=\frac{\text{R}}9{}$

Resistance becomes $\frac{1}{9}\text{th}.$

$\text{R}=\rho\frac{\text{I}}{\text{A}}$

$\rho\rightarrow3\rho$

$\text{R}'=3\rho\frac{\text{I}}{\text{A}}=3\text{R}$

Resistance becomes 3 times.

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