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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 R3.

Step by step solution

01

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=ρLA

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

02

Calculation of resistance

Consider the two resistance R1and R2such that there ratio is:

R1R2=ρρ×L1L2×A2A1

Consider the area of the cylindrical cross section is A=πr2.

R1R2=L3L×πr22πr12

Solve further as,

R1R2=13×3r2r2R2=R3

Hence, the resistance is R3.

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