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Chapter 4: Q2DQ (page 840)

Question: 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

Answer

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=蚁尝A

Here, is 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 R1 and R2 such that there ratio is:

R1R2=蚁蚁脳L1L2脳A2A1

Consider the area of the cylindrical cross section is A=蟺r2.

R1R2=L3L脳蟺r22蟺r12

Solve further as,

R1R2=13脳3r2r2R2=R3

Hence, the resistance is R3.

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