You are presented with several wires made ofthe same conducting material. The radius and drift speed are givenfor each wire in terms of some unknown units \rm r and \rm v. Rank thewires in order of decreasing electron current.
Rank from most to least electroncurrent. To rank items as equivalent, overlap them.
radius=1 radius=4 radius =2 radius= 3
drift speed =5V drift speed = .5V drift speed = 2.5V drift speed = 1 V

Respuesta :

Answer:

The ranking of current from the most to the least is [tex]I_{3} >I_{4}> I_{2}> I_{1}[/tex]

Explanation:

Case Number  1 :

Drift velocity=[tex]V_{drift}[/tex]= 5v

Radius=r= 1r

Square of radius=[tex]r^{2}[/tex]= 1

Current=[tex]I=C(V _{drift} *r^{2} )[/tex]=C(5v[tex]r^{2}[/tex])

Case Number 2 :

Drift velocity=[tex]V_{drift}[/tex]=0.5v

Radius=r=4r

Square of radius=[tex]r^{2}[/tex]=16

Current=[tex]I=C(V _{drift} *r^{2} )[/tex]= C(8v[tex]r^{2}[/tex])

Case number 3 :

Drift velocity=[tex]V_{drift}[/tex]=2.5

Radius=r=2r

Square of radius=[tex]r^{2}[/tex]=4

Current=[tex]I=C(V _{drift} *r^{2} )[/tex]= C(10v[tex]r^{2[/tex])

Case number 4:

Drift velocity=[tex]V_{drift}[/tex]=1v

Radius=r=3r

Square of radius=[tex]r^{2}[/tex]=9

Current=[tex]I=C(V _{drift} *r^{2} )[/tex]=C(9v[tex]r^{2[/tex])

Hence, The ranking of current from the most to the least is [tex]I_{3} >I_{4}> I_{2}> I_{1}[/tex]

Answer:

So in order of most to least electric current,

Ic > Id > Ib > Ia

Explanation:

Let the wires be represented as A, B, C, D

in the the given order.

So wire A has radius 1 and drift speed = 5V

wire B has radius 4 and drift speed = 0.5V

wire C has radius 2 and drift speed = 2.5V

wire D has radius 3 nd drift speed = 1V

The current in a given wire is directly proportional to the cross seectional area A(πr²) and also to the drift speed v

I = nqvA

Assuming n and q are constant,

I ∝v× r²

Ia = C×5v × r² = 5Cvr²

Ib = C×0.5v × (4r)² = 8Cvr²

Ic = C×2.5v× (2r)² = 10Cvr²

Id = C×1v×(3r)² = 9Cvr²

Where Cis a constant = nqπ

So in order of most to least electric current,

Ic > Id > Ib > Ia

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