Current electricity

Drift velocity:

Draft velocity of electron:
Metallic conductor there are large no. of free electron and these free electron are responding only for carrying electricity through the conductor. In the absence of the electric field the resultant velocity of the electron in a particular direction is zero and hence the net transport of charge is also zero and the current don’t flow through the conductor in the absence of electric field.

But if the electric field is applied then the electron start to accelerate in the opposite direction of the field applied so, the velocity of the electrons increase which implies that K.E. of the electron also increases. When these electrons collide with the atoms or ions then the velocity of electrons decrease by transformation of energy to the atoms or ions this process is continuous and the average acceleration of an electron is ceases i.e. reduced to zero. Then the electron required a constant velocity to the opposite direction of the field applied. This constant velocity of the electron on the opposite direction of the field is called drift velocity of the electron.
Relation between the electric current and drift velocity:
Let us consider a conductor having length L, cross-sectional area A, containing ‘n’ no. of electron per unit volume, having charge e in each electron.  

Volume of the given conductor =AL
Total no. of free electron in given conductor ( Q)=nAL
Total no. of the charge in given conductor= nALe
If the external source is connected to the conductor then charge starts to flow through the conductor. Let Vd be the drift velocity of the electron, Q be the charge passes through the length of conductor L in the time t.I be the current passes through the conductor is given by
I=Qt$\frac{\mathrm{Q}}{\mathrm{t}}$ =neALt$\frac{\mathrm{L}}{\mathrm{t}}$ = neAVd where Vd = L/t  (Vd is called drift velocity of electron).
This is the expression forRelation between the electric current and drift velocity.
Since current density, J = I/A then we have from above expression
J =VRA$\frac{\mathrm{V}}{\mathrm{R}\mathrm{A}}$  = VρLAA$\frac{\mathrm{V}}{\frac{\rho \mathrm{L}}{\mathrm{A}}\mathrm{A}}$  = Eρ$\frac{\mathrm{E}}{\rho }$  = σ E
∴ J = σ E

Ohmic and non-ohmic conductor:
The conductors which obey ohm’s law strictly are called Ohmic conductors.
The conductors which do not follow ohm’s law are called non – ohmic conductors.
Ohms’ law:
It states that the electric current flowing through any conductor is directly proportional to the potential difference between the ends of the conductor, under constant physical condition (temperature, pressure, etc.)

Let I be the electric current flowing through any conductor and V be the potential difference between the ends the conductors. So, according to Ohm’s law, we can write:
V ∝ I.
Or, V = RI
Where, R is proportionality constant called resistance of the conductor.
Verification:
The experimental arrangement for verification of Ohm’s law is shown in figure. A and V stands for Ammeter and Voltmeter. Xh for Rheostat.
Here, by varying the Rh, the electric current (I) and potential difference across any length of conductor is measured from Ammeter and Voltmeter respectively. We plot V versus I. If the plot is a straight line passing through origin i.e. of the form y = mx then Ohm’s law is said to be verified.
The resistivity of the material:
The resistivity of the material of a conductor is defined as the resistance per unit length per unit area of cross – sectional of the conductor.
Its unit is ohm meter.
Shunt:
Shunt is a low resistance connected in parallel with resistance of a galvanometer while converting galvanometer into ammeter.
Conservation of galvanometer in to ammeter:
Let us consider the resistance of the galvanometer is G, the maximum current measured by the ammeter is I, and the maximum current measure by the galvanometer by passing through it is Ig, then the current passes through the small resistance i.e. shunt S is (I-Ig) as shown in

Since the resistance of the galvanometer and shunt are in parallel then a/c to the property of parallel combination we have,
Potential difference across shunt= Potential difference across galvanometer
                                           (I-Ig)S=IgG
                                    Or, S = (IgG)/ (I-Ig)……………..1
Hence equation 1 gives the value of shunt.
Since the S and G resistance are in parallel then the effective resistance of ammeter (RA)  is given by
$\frac{1}{{\mathrm{R}}_{\mathrm{A}}}$=1S+1G$\frac{1}{\mathrm{S}}+\frac{1}{\mathrm{G}}$=G+SGS$\frac{\mathrm{G}+\mathrm{S}}{\mathrm{G}\mathrm{S}}$ or, RA=GSG+S$\frac{\mathrm{G}\mathrm{S}}{\mathrm{G}+\mathrm{S}}$

This show the resistance of ammeter (RA) very smaller (lower) then that of shunt S. So, when it is connected ammeter is connected in series in circuit then there is no effect the on current passing through the circuit.

Conservation of galvanometer in to Voltmeter:
A voltmeter is a device used to measure potential difference between two points in a circuit. It is connected across two points between which the potential difference is to be measured. By connecting a voltmeter in a circuit must not change the current and hence the potential difference in the circuit, a voltmeter should have very high resistance, ideally infinite resistance. Such p.d. measuring device can be made by connecting a very high resistance in series with a galvanometer.

Let G be the resistance of galvanometer and Ig current producing the maximum deflection in the galvanometer. To measure the maximum voltage, V by the voltmeter, the high resistance R is connected in series. So,
V = Ig (R + G)
Or, IgR = V – IgG.
Or, R = VIg−G$\frac{\mathrm{V}}{{\mathrm{I}}_{\mathrm{g}}}-\mathrm{G}$
This equation gives the value of resistance R, which has connected in series to the galvanometer, and this connection converts the galvanometer into voltmeter of range u – V volts. The effective resistance of the voltmeter RV = R + G. Since, R is high, the resistance of the voltmeter RV is high and it will not draw much current from the circuit.
Ohmmeter:
Ohmmeter is an arrangement which is used for measuring resistance.
Potential Divider:
A potential divider is an arrangement of resistor in series across a given p.d to provide a known fraction of the potential difference.

There is large no. of free electron continuously move from lower potential to higher potential. 

On the way or during motion the electron suffer collision with the positive ions of the conductor at that situation electron looses some of the energy. As in that way there are no. of collision and they loose more energy and due to lose of the energy electron cannot gets it actual velocity the net effect is that the electron drift with small velocity called drift velocit.