A conducting wire has a resistivity

In summary, the resistance of a conducting wire with resistivity ρ as a function of length L and cross-sectional area A is given by r=(ρ0)(L^2)/A. However, for a very short length ΔL, the resistance ΔR is given by ΔR=(ρ0)(L)(ΔL)/A.
  • #1
Jay9313
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0

Homework Statement



A conducting wire has a resistivity, ρ as a function of its length, L, given by ρ=(ρ0)(L) where (ρ0) is constant. A is the cross-sectional area of the wire. the resistance of the wire would be
A) [(ρ0)(L)]/A
B) (ρ0)/(2A)
C) [(ρ0)(L)]/(2A)
D) [2(ρ0)(L^2)]/A
E) [(ρ0)(L^2)]/(2A)


Homework Equations


r=(ρL)/A



The Attempt at a Solution


r=[(ρ0)(L^2)]/A

Am I missing something?
 
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  • #2


Jay9313 said:

Homework Statement



A conducting wire has a resistivity, ρ as a function of its length, L, given by ρ=(ρ0)(L) where (ρ0) is constant. A is the cross-sectional area of the wire. the resistance of the wire would be
A) [(ρ0)(L)]/A
B) (ρ0)/(2A)
C) [(ρ0)(L)]/(2A)
D) [2(ρ0)(L^2)]/A
E) [(ρ0)(L^2)]/(2A)

Homework Equations


r=(ρL)/A

The Attempt at a Solution


r=[(ρ0)(L^2)]/A

Am I missing something?
Yes.

For a (very short) length, ΔL, of wire, the resistance, ΔR is given by, [itex]\displaystyle \Delta R=\rho\frac{\Delta L}{A}=\left(\rho_0 \cdot L\right)\frac{\Delta L}{A}\,.[/itex]
 

Related to A conducting wire has a resistivity

1. What is resistivity?

Resistivity is a measure of a material's ability to resist the flow of electric current. It is represented by the Greek letter rho (ρ) and is measured in ohm-meters (Ω·m).

2. How does resistivity affect a conducting wire?

A conducting wire's resistivity determines its resistance to the flow of electric current. The higher the resistivity, the greater the resistance and the more difficult it is for current to flow through the wire.

3. What factors can affect the resistivity of a conducting wire?

The resistivity of a conducting wire can be affected by its material, temperature, and dimensions. Different materials have different resistivities, and as temperature increases, resistivity typically increases as well. The length and cross-sectional area of the wire can also impact its resistivity.

4. How is resistivity measured?

Resistivity is typically measured using a device called an ohmmeter, which applies a known voltage to the wire and measures the resulting current. The resistivity can then be calculated using the formula ρ = RA/L, where R is the resistance of the wire, A is its cross-sectional area, and L is its length.

5. What are some real-world applications of resistivity in conducting wires?

Resistivity is an important factor in many electrical devices and systems. It is used in the design of wires and cables, as well as in the development of electrical components such as resistors and capacitors. It also plays a role in determining the efficiency of power transmission and distribution systems.

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