Find the resistivity of the resistive wire

In summary, the equation ##ρ=\frac{RA}{L}## is used to calculate the resistivity, and the equations ##I=\frac{ΔQ}{Δt}## and ##I=\frac{ΔV}{R}## are used to calculate current. The calculated values for resistivity, equivalent resistance, current, and charge are 3.978×10-6 Ωm, 12 Ω, 3 A, and 300 C respectively.
  • #1
Fatima Hasan
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Homework Statement


Capture.png


Homework Equations


##ρ=\frac{RA}{L}##
##I=\frac{ΔQ}{Δt}##
##I=\frac{ΔV}{R}##

The Attempt at a Solution


(a)
##ρ=\frac{RA}{L}##
##L=\frac{2*π*r}{2} = πr##
ρ = (5*2.5*10-7)/(π*0.1)
ρ = 4*10-6 Ωm.

(b)
Req = 7+5 = 12Ω
##I=\frac{ΔV}{R}##
I = 36/12 = 3 A
##I=\frac{ΔQ}{Δt}##
3 = ΔQ / 100
ΔQ = 3*100 = 300 C

Is my answer correct ?
 

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  • #2
Fatima Hasan said:

Homework Statement


View attachment 225595

Homework Equations


##ρ=\frac{RA}{L}##
##I=\frac{ΔQ}{Δt}##
##I=\frac{ΔV}{R}##

The Attempt at a Solution


(a)
##ρ=\frac{RA}{L}##
##L=\frac{2*π*r}{2} = πr##
ρ = (5*2.5*10-7)/(π*0.1)
ρ = 4*10-6 Ωm.

(b)
Req = 7+5 = 12Ω
##I=\frac{ΔV}{R}##
I = 36/12 = 3 A
##I=\frac{ΔQ}{Δt}##
3 = ΔQ / 100
ΔQ = 3*100 = 300 C

Is my answer correct ?
Yes, but the resistivity comes out to be 3.978×10-6 ohm-meter. You might not get full credit if you round that off to 4.
 
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Likes berkeman and Fatima Hasan

1) What is resistivity?

Resistivity is a measure of how strongly a material opposes the flow of electric current. It is represented by the Greek letter rho (ρ) and is measured in ohm-meters (Ω∙m).

2) How is resistivity different from resistance?

Resistance is a measure of the difficulty for current to flow through a material, while resistivity is a property of the material itself. Resistivity takes into account the dimensions and composition of the material, while resistance does not.

3) How do you calculate resistivity?

Resistivity can be calculated by dividing the resistance of a material by its cross-sectional area and then multiplying by its length. The formula is ρ = RA/l, where ρ is resistivity, R is resistance, A is cross-sectional area, and l is length.

4) What factors affect the resistivity of a material?

The resistivity of a material is affected by its composition, temperature, and impurities. Generally, materials with higher resistivity are poor conductors, while materials with lower resistivity are good conductors.

5) How can I measure the resistivity of a resistive wire?

The resistivity of a resistive wire can be measured using a multimeter. First, measure the resistance of the wire using the multimeter. Then, measure the length and cross-sectional area of the wire. Finally, use the resistivity formula (ρ = RA/l) to calculate the resistivity of the wire.

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