Current Electricity
Rate of flow of charge through any cross-section of a wire is called Electric current. Thus,
So if DQ charge passes through a cross-section of a conductor in time Δt then the average electric current through the area during this time as
The current at time t is (instantaneous current)
Current is a scalar quantity. It's S.I. unit is ampere (A) and C.G.S. unit is emu and is called biot (Bi), or ab ampere. 1A = (1/10) Bi (ab amp.) The direction in which the positive charge will flow gives the direction of conventional current.
Note:
- In conductor the current is caused by electron (free electron). The no. of electron (negative charge) and proton (positive charge) in a conductor is same. Hence the net charge in a current carrying conductor is zero.
- In solid conductors like metals current carriers are free electrons.
- In liquids current carriers are positive and negative ions.
- In gases current carriers are positive ions and free electrons.
- In semi conductors current carriers are holes and free electrons.
Types of Electric Current
The electric current may be classified into three main classes:
- Steady current
- Varying current
- Alternating current
Steady Current: When the magnitude of current does not change with time, it is called a steady current. The following figure shows the graph between steady current and time. Note that value of current remains the same as the time changes. The current provided by a battery is almost a steady current.
Varying Current: When the magnitude of current changes with time, it is called a varying current. The above figure shows the graph between varying current and time. Note that value of current varies with time.
Alternating Current:An alternating current is one whose magnitude changes coninuously with time and direction changes periodically. Due to technical and economical reasons, we produce alternating currents that have sine waveform (or cosine waveform) as shown in above figure. It is called alternating current because current flows in alternate directions in the circuit, i.e,. from O to T/2 second (T is the time period of the wave) in one direction and from T/2 to T second in the opposite direction.
Current Density (J)
Current flowing normally through unit area of cross-section is called current density. It is a vector quantity, and is represented by `j'.
Situation I: If a current `i' is distributed uniformly over area S, then the current density 
.
Situation II: If area S which makes some angle with the electric current (figure b). If the normal to the area makes an angle q with the direction of the current, the current density is,
or 
From above two situations it is clear that 
For a finite area, 
Note: Electric current has direction as well as magnitude but it is not a vector quantity. It does not add like vectors. The current density is a vector quantity.
Illustrations
How many electrons pass through a lamp in one minute, if the current is 300 mA? Given, charge on electron = 1.6 ´ 
C.
Solution: Here, I = 300 mA = 300 ´ 
A;
e = 1.6 ´ 
C; t = 1 minute = 60 s
The charge passing through lamp in one minute,
C
Suppose that n electrons pass through the lamp in one minute. If e is charge on an electron, then
=1.125´ 1020
In hydrogen atom, electron revolves around the nucleus along a path of radius 0.51 Å making 6.8 ´ 
revolutions per second. Calculate the equivalent current. Given charge on electron = 1.6 ´ 
C.
Solution: Here, e = 1.6 ´ 
C; v = 6.8 ´ 
revolutions s
; r = 0.51 Å = 0.51 ´ 
m
If T is time period of electron, then it crosses a point on its circular path after T seconds. Hence, equivalent current,
´ 6.8´
=1.088´103A
The space between the plates of a parallel plate capacitor is completely filled with a material of resistivity 2×1011 W-m and dielectric constant 6. Capacity of the capacitor with the given dielectric medium between the plates is 20 nF. Find the leakage current if a potential difference 2500 V is applied across the capacitor.
Solution: Charge on the capacitor, Q = CV= 20×109 × 2500 = 5 × 105C
Surface charge density, 
And electric field strength between the plates, 
and current 
= 4.7 µA
Drift Speed
If electric field is applied across the metal, electrons experience a force opposite to the field. The electrons get biased in their random motion in favour of the force. As a result, the electrons drift slowly in this direction. At each collision, the electron starts afresh in a random direction with a random speed but gains an additional velocity v' due to the electric field. This velocity v' increases with time and suddenly becomes zero as the electron makes a collision with the lattice and starts afresh with a random velocity.
As the time t between successive collisions in small, the electron slowly and steadily drifts
opposite to the applied field. If the electron drifts a distance l in a long time t, we define drift speed as 
It 
be the average time between successive collisions, the distance drifted during this period is
The drift speed is 
As 
is the average of drift velocities of large number of electrons at same instant and as for each electron 
with 
= constant
Drift speed is proportional to the electric field E and to the average collision time 
.
Note: 1. When no electric field exists in a conductor, the free electrons only moves with random velocity 
and when a field E exists, they move with a drift velocity along with random velocity.
i.e. 
2. Drift velocity is of the order of 105 m/s where as the random speed is of the order of 106 m/s. So this clears that drift velocity is very small with respect to random speed.
Relation Between Drift Speed and Current Density 
Consider a length 
of the conductor. The volume of this portion is 
If there are n free electrons
per unit volume of the wire, the number of free electrons in this portion is 
. All these electrons cross the area A in time 
. Thus, the charge crossing this area in time 
is
or
and 
Important Points
The direction of drift velocity for electron in a metal is opposite to that of applied electric field (i.e. current density 
).
i.e., greater the electric field, larger will be the drift velocity.
When a steady current flows through a conductor of non-uniform cross-section drift velocity varies inversely with area of cross-section 
If cross-section is constant, I µ J i.e. for a given cross-sectional area, greater the current density, larger will be current.
The drift velocity of electrons is small because of the frequent collisions suffered by electrons.
In the absence of electric field, the paths of electrons between successive collisions are straight line while in presence of electric field the paths are generally curved.