Chapter 4: Q2DQ (page 840)

A cylindrical rod has resistance $R$ . If we triple its length and diameter, what is its resistance in terms of R

Short Answer

Expert verified

The value of the resistance is $\frac{R}{3}$ .

Step by step solution

Definition of Resistance

The term resistivity is opposition offered by the particular electric conductor to the flow the charges. It depends on the type of material used, while the resistance will depend on the length and the area of the conductor.

The expression for the resistance is,

$R = \frac{ρL}{A}$

Here, $ρ$ is the resistivity, Ris the resistance, L is the length and A is the area of the cross section.

Calculation of resistance

Consider the two resistance $R_{1}$ and $R_{2}$ such that there ratio is:

$\frac{R_{1}}{R_{2}} = \frac{ρ}{ρ} \times \frac{L_{1}}{L_{2}} \times \frac{A_{2}}{A_{1}}$

Consider the area of the cylindrical cross section is $A = {πr}^{2}$ .

$\frac{R_{1}}{R_{2}} = \frac{L}{3 L} \times \frac{{πr}_{2}^{2}}{{πr}_{1}^{2}}$

Solve further as,

$\frac{R_{1}}{R_{2}} = \frac{1}{3} \times \frac{{(3 r)}^{2}}{r^{2}} R_{2} = \frac{R}{3}$

Hence, the resistance is $\frac{R}{3}$ .

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A cylindrical rod has resistance $R$ . If we triple its length and diameter, what is its resistance in terms of R

Short Answer

Step by step solution

Definition of Resistance

Calculation of resistance

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A cylindrical rod has resistance R. If we triple its length and diameter, what is its resistance in terms of R

Short Answer

Step by step solution

Definition of Resistance

Calculation of resistance

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Astrophysics

Work Energy and Power

Nuclear Physics

Force

Linear Momentum

Study anywhere. Anytime. Across all devices.

A cylindrical rod has resistance $R$ . If we triple its length and diameter, what is its resistance in terms of R