20.3 Resistance and Resistivity

The resistances of two wires having the same lengths and cross section areas are 3 Ω and 11 Ω. If the resistivity of the 3 Ω wire is 2.65 × 10⁻⁸ Ω∙m, find the resistivity of the 1 Ω wire.

Suppose the resistance of a wire is 2 Ω. If the wire is stretched to three times its length, what will be its resistance? Assume that the volume does not change.

What is the resistance of a 20.0-m-long piece of 12-gauge copper wire having a 2.053-mm diameter?

If the 0.010-mm diameter tungsten filament in a light bulb is to have a resistance of $\text{0}.\text{200 }\Omega$ at $20.00º \text{C}$, how long should it be?

What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when $1.00 × 10^{\text{3}} \text{V}$ is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at $\text{20} . 0º \text{C}$. Over what temperature range can it be used?

An electronic device designed to operate at any temperature in the range from $–\text{10} . 0º \text{C to 55} . 0º \text{C}$ contains pure carbon resistors. By what factor does their resistance increase over this range?

Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at $\text{20} . 0º \text{C}$?

A copper wire has a resistance of $0 . \text{500 } \Omega$ at $\text{20} . 0º \text{C}$, and an iron wire has a resistance of $0 . \text{525 } \Omega$ at the same temperature. At what temperature are their resistances equal?

(a) Redo the exercise taking into account the thermal expansion of the tungsten filament. You may assume a thermal expansion coefficient of $\text{12} \times \text{10}^{- 6} / º\text{C}$. (b) By what percentage does your answer differ from that in the example?