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?

Q: 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?

$\text{R}=\rho\frac{\text{I}}{\text{A}}$ 1. I → 3I $\text{R}'=\rho\frac{3\text{I}}{\text{A}}=3\text{R}$ Resistance gets tripled. 2. 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 $\frac{1}{9}\text{th}.$ 3. $\text{R}=\rho\frac{\text{I}}{\text{A}}$ $\rho\rightarrow3\rho$ $\text{R}'=3\rho\frac{\text{I}}{\text{A}}=3\text{R}$ Resistance becomes 3 times.

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?

Download our app for free and get started

Solution

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

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.

Download our app
and get started for free

Similar Questions

Download our appand get started for free

Similar Questions

Download our app
and get started for free