# Electric Current - 1

We all must be families with the team electric current. We think who simple it is. But when even for a single moment we try to analyze actually what it is, how is it generated then we realize that team and making it so simpler to us. Now a days every single thing is an application of current and electricity.

__Conductor for and time is called electric current__

Where dq is the charge flown through a cross section area conductor in time dt. It is also called instantaneous current I this dt - 0.

Where q is the charge flown in a finite time t. S.I unit of electric current is Ampere (A).

__Illustration - 1.__ The current in a wire varies with time according to the relation.

I=(3+2t)A

(a) How many coloumbs of charge pars a cross section of the wi in the time interval between t=0 and t=4s ?

(b) What constant current would transport the same charge in the same time interval ?

__Ans :-__(a) We know that,

(b) Let the new current be I.

Current density is defined as.

Note that it is a vector quantity.

The direction of is same as direction of current. If a uniform current i moves over an area S and is in same direction as area vector then,

So i is a resulting from the dot product of and .

__Drift Velocity -__ It is defined as.

Where e = electron charge.

m = mass of electron

E = Electric field

= average collision time.

to the field direction. But in their way they collide with of positive ions. So they follow a very zig-zag motion, hence length that they drift even in a long interval in small let this length be ‘l’ and time interval = ‘’. then -

Now the electron moves under the influence of an electric field, Hence

Where

depends on temperature and material of conductor

__Current and drift velocity :-__ We can express a relation in current and drift velocity as,

where n = Moving charged particles per unit volume.

A = Area of cross section perpendicular to current flows.

__Dumb Question - 3.__ What is the direction of current density ?

__Ans:-__ being a vector have a direction similar to .

__Dumb Question__ - 4. It a charge (q) is rotating with frequency f. What is the current ?

__Ans __:- I = qf because the units of current is amp = coloumb/s and qf constitutes this unit.

to electric field () with constant of proportionality being resistivity of (P) of the material, at a constant temperature.

This relationship is called ohm’s law.

Where V is the potential difference across the conductors.

placing J and E is equation (1) -

now,

this or resistance

which is more general form of ohm’s law.

__Question :-__ Is ohm’s law for all materials ?

__Ans :-__ The current density in a conductor depends on the electric field and on the properties of the material. In general this dependence is quiet complex But for same materials, especially metals, at a constant temperature ohm’s law holds good.

__Illustration - 2.__ If a wire of resistance R is streched to double its length. What will be new resistance ?

__Ans :-__ Suppose initial radius of wire be r, final be r’ and new length be l’ (= 2l)

Now, after streching volume of wire will not change :-

New changed Area = where A = initial area

New resistance

__Temperature dependence of resistivity and resistance.__

The resistivity of a metallic conduct or nearly increases with increase in temperature.

__Reason - __

With the increase in temperature the ions of conductor vibrate with greater amplitude and the collision between electrons and ions be come more frequent.

where P_{0} = resistivity at a reference temperature.

T_{0} = The factor is called the temperature co-efficient of resistivity.

The resistance of a given conductor depends on P, A and l. Ad temperature changes A and l also changes but these changes are quiet small and thus may be treated as constant.

__KIRCHOFF’S LAWS__

(1)__Junction law__

It states that the net current entering a junction is equal to net current exiting that junction.

Or, Algebric sum of the current is into any junction is zero.

In this fugure,

i_{1} + i_{2} = i_{3} + i_{4} + i_{5}

2) __Voltage/Loop Law__

It states that algebric sum of the potential drop around any closed path is zero.

__Sign Convention__:

When we travel through a source in the direction from to+, the voltage is considered to be positive, when we travel from + to.

For Battery

= V_{B} - V_{A} = + E

V_{B} - V_{B} = - t

For resistance

= V_{B} - V_{B} = - IR

V_{B} - V_{A} = + IR

__Dumb Question - 7.__ What are the basic principles on which kirchoff’s laws are based ?

__Ans :-__ Kirchoff’s junction rule basically supports the law of __conservation of change.__ On the other hand, kirchoff’s second law that is kirchoff’s voltage rule or kirchoff’s loop rule is based on the law of __conservation of energy.__