Electric Current

[sssamudra98]

i = dq/dt
so for a conductor of length L, maintained at constant potential difference, we know that q = enAL
where e is charge on electron
n is electrons per unit vol.
A is area of cross section of conductor
SO
in q = enAL what is changing with time so that we come across rate of change of charge

[studiot]

This is a very important technique in Engineering and you have posted in the Engineering section.

 

What you have is a control volume and your equation is not quite right for n, since they electrons at the start of the period are not the same as the eelctrons at the end ie you have electrons entering and leaving the control volume over the period so the current is the rate of electrons crossing a boundary surface.

 

If you like n = dn/dt (leaving) - dn/dt (entering)

 

this control volume idea is important in

Thermodynamics (heat flow)

Fluid mechanics

Electricity

 

and comes under the heading transport phenomenon.

 

Momentum may be transported as well as mass and heat.

Edited July 2, 2015 by studiot

[sssamudra98]

you mean to say in q = neAL nis causing variation in q ??

 

AND what if A (area of cross section) is also varying ??

[studiot]

I can move the goalposts too.

 

What if L is varying?

 

Is this a serious question or a windup?

[sssamudra98]

i am not understanding what you are trying to say

can you please define current in light of my doubt

this doubt pinching me since long

without having cleared this i cannot proceed

please help me

[studiot]

You have not responded to my first answer.

[sssamudra98]

What if L is varying ?

 

varying L will vary q

Actually i want to ask

I=dq/dt? so, for every charge leaving the cross-section of the conductor, an equivalent one will enter. This means that across the cross-section dq/dt, the summed change of charge with respect to time, equals 0!

[studiot]

 

I=dq/dt? so, for every charge leaving the cross-section of the conductor, an equivalent one will enter. This means that across the cross-section dq/dt, the summed change of charge with respect to time, equals 0!

 

 

Of course it does.

 

The rate of charge entry equals the rate of charge exit.

 

So the rate of accumulation of charge is zero.

 

The summed charge is not the same as the accumulation of charge; the summed charge must include all charge entering and leaving the control volume in the time period.

[Sensei]

What if L is varying ?

 

varying L will vary q

 

If you will change length L, resistance R will change.

The higher L, the bigger resistance R.

 

Take a play with resistance wire, and check resistance with multimeter at different distances from the beginning..

They are sold per meters.

Like f.e. 100 Ohms per meter.

http://www.ebay.com/bhp/resistance-wire