Table of contents  
What is Electric Current?  
Electric Current in Conductors  
What is Ohm's Law?  
Drift of Electrons  
Derivation of Expression of Drift Velocity  
Mobility  
Current Density  
Solved Examples 
Think about everything you do in a day. From using your phone to turning on lights, electricity is what makes it all possible. But have you ever wondered how it all works? Well, it is all possible due to something called electric current.
In the first unit on 'Electrostatics', we studied the characteristics of charges at rest. However, most of the practical applications of electricity involve charges in motion. For instance, an electric bulb glows when charge flows through it, and an electric fan rotates when charges are made to pass through the coil.
Electric Current
Electric current is defined as the speed at which electrons move through a conductor, with its measurement unit being the Ampere in the International System of Units (SI).
Electrons are tiny constituents found within the molecular framework of matter. Their mobility varies depending on how tightly they are bound to the nucleus of an atom. When electrons are loosely bound, they have the freedom to move within the material. Since electrons carry a negative charge, their movement constitutes an electric current. The conductivity of a substance is determined by the extent to which electrons can move within it.
If charge dq passes through an imaginary surface in time dt, then the current I through that surface is defined as I= dq/dt. This is the instantaneous current. The direction of the current is the direction of flow of positive charge carriers, or opposite to the flow of electrons.
Current is a scalar quantity. Though electric current represents the direction of flow of positive charge, still, it is still treated as a scalar quantity. This is because electric current follows laws of scalar addition and not vector addition. The angle between the wires carrying electric current does not affect the total current in the circuit.
Some things have electrons that aren't tightly held. These electrons can move easily and are called free electrons or conduction electrons. When in an electric field, they move against it. Materials with these electrons are called conductors.
Conductors
Some things are called insulators. In these, electrons stick closely to atoms and there are no free electrons. When in an electric field, electrons may shift a bit but can't move far from their atoms. These materials are also called dielectrics.
Insulators
Semiconductors act like insulators when their temperature is low, but as the temperature rises, a few electrons can break free and conduct electricity in response to an electric field.
 Their behavior isn't only influenced by temperature but also by doping, which introduces impurities to tweak their electrical properties.
 When an electron is freed in a semiconductor, it leaves a hole behind, and these holes also play a role in conducting electricity in semiconductors.
Semiconductors
There are two types of electric currents: Alternating Current (AC) and Direct Current (DC).
Representation of AC and DC Currents
According to Ohm’s Law, the current flowing through a wire is directly proportional to the voltage applied at the ends of the wire provided that the temperature and conductivity remain the same.
V ∝ I
Upon removing the proportionality sign, a proportionality constant is introduced known as Resistance(R).
Where,
V is Voltage at the ends of conductor
R is Resistance offered by the conductor
I is Current through the wire
Ohm's Law
A conductor contains a large number of loosely bound electrons called free electrons or conduction electrons. These electrons move randomly in all directions within the entire volume of the conductor, and in this process keep on colliding with the atoms/molecules/ions of the conductor, changing their direction of motion at each collision.
When current is applied across the conductor the randomly moving electrons are subjected to electrical forces along the direction of the electric field.
Motion of free electrons (a) in the absence of an electric field (b) in the presence of an electric fieldDue to this electric field, free electrons still have their random moving nature, but they will move through the conductor with a certain amount of force. The net velocity in a conductor due to the moving of electrons is referred to as the drift of electrons.
When no electric field is applied across a conductor, the direction of motion of free electrons is so randomly distributed that the average thermal velocity of electrons is zero.
At any given time, an electron has a velocity,
v_{1} = u_{1 }+ aτ_{1}
where u_{1} is the thermal velocity of the electron, a is the acceleration caused by to electric field and τ_{1} is the time elapsed since it has suffered the last collision with an atom/ ion and is called relaxation time.
Similarly, the velocities of the other electrons are
The average velocity of all the free electrons in the conductor is equal to the drift velocity v_{d} of free electrons:
Here the first expression is taken as zero because it represents the average thermal velocity of the conductor which is always zero.
τ represents the average relaxation time. Its value is of the order of 10^{14} seconds. The negative sign in the expression of drift velocity shows that its direction is always opposite to that of the applied electric field.
Let n = number density of free electrons and A = area of crosssection of the conductor
Number of free electrons in the conductor of length L = nAL,
The total charge on these free electrons Δq = neAvd
Time taken by drifting electrons to crossconductor
Conductivity arises from mobile charge carriers. In metals, these mobile charge carriers are electrons; in an ionized gas, they are electrons and positively charged ions; in an electrolyte, these can be both positive and negative ions.
Current density refers to the density of current flow in some conductors. It is denoted by the symbol J. Current Density and its measurement are very important as it is the measure of the flow of electric charge in amperes per unit area of crosssection i.e. m².
If the crosssectional area is not normal to the current but makes an angle θ with the direction of the current
Current density is a vector quantity. Its direction is the same as that of Its S.I. unit is ampere/m^{2} and dimension [L^{–2}A^{1}].
Q1. If the instantaneous current in a metallic wire is i=(5+10t)A then find the amount of charge flown through it from t=2s to t=3s.
Solution:
Given the instantaneous current,
Therefore, the current flowing through the wire from t=2s to t=3s is 60C  30C = 30C
Q2. The figure below shows a plot of current I through the crosssection of a wire over a time interval of 10s. Find the amount of charge that flows through the wire during this period.
Solution:
Amount of Charge that flows in 10 seconds is = area under I  t graph
= area of triangle + area of sqaure
= (1/2 x base x height) + (side x side)
= (1/ 2 × 5 × 5) + (5× 5) = 12.5 + 25 = 37.5 C
Q3. If n =8.5 × 10^{28} m^{–3}, how long does an electron take to drift from one end of a 3 m long wire to its other end? The area of the crosssection of the wire is 2.0 × 10^{6} m^{2 }and it carries a current of 3.0 Ampere. (JEE Mains 2019)
Solution:
For constant p.d. across the conductor, the electrons drift with constant drift velocity across it.
If we find the drift velocity, the time to drift across wire of constant length is easily found out
Given that:
(i) Number density n = 8.5 × 10^{28} m^{–3} (ii) Crosssectional area A = 2.0 × 10^{6}m^{2}
(iii) Current I = 3 A (iv) Charge on electron e = 1.6 × 10^{–19} C
Current in terms of drift speed is expressed as I = neAv_{d} ⇒ v_{d} = I/neA
Now time taken to cross the length ℓ of the wire is:
t= ℓ/v_{d} = neAℓ/I = (8.5 × 10^{28}x 1.6 × 10^{–19}x 2.0 × 10^{6 }x 3) / 3 = 2.7 x 10^{4} s
Q4. What is the drift velocity for the electrons in a conductor when an electric field of strength 200 V/m is applied to it and the mobility of electrons is 4.5 x 10^{6} m^{2}s^{1}V^{1}?
Solution:
Here, E= 200 V/m ; µ= 4.5 x 10^{6} m^{2}s^{1}V^{1}
Therefore, drift velocity, v_{d}
v_{d} = µE
= 4.5 x 10^{6} x 200
= 9.0 x 10^{4} m/s
Q5. A current of 5 A passes through a copper conductor (resistivity = 1.7×10 ^{– 8}Wm) of radius of crosssection 5 mm. Find the mobility of the charges if their drift velocity is 1.1×10 ^{– 3} m/s.
(a)1.8m^{2}/Vs (b)1.5 m^{2}/Vs (c)1.3 m^{2}/Vs (d) 1.0 m^{2}/Vs
(JEE Mains, 2019)
Solution:
105 videos425 docs114 tests

1. What is electric current and how is it related to the drift of electrons in conductors? 
2. What is Ohm's Law and how is it related to electric current? 
3. How is drift velocity derived and what factors affect it? 
4. What is mobility and how does it relate to the drift of electrons in a conductor? 
5. How is current density calculated and what does it represent in the context of electric current? 

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