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Flow of Electric Charges in Metallic Conductors

Complete conceptual guide for CBSE Class 12, NEET, JEE Main, JEE Advanced, Olympiad Physics, AP Physics, IB Physics and A-Level Physics.

CBSENEETJEE MainJEE AdvancedOlympiadAPIBA-Level

Section 1: Introduction to Electric Current

Electric current is the rate at which electric charge crosses a given cross-section. In metallic conductors, free electrons are the mobile charge carriers. When no electric field is applied, electrons move randomly and no net current is produced. When a potential difference is applied, an electric field develops and electrons acquire a small drift velocity.

Conventional Current

Direction in which positive charge would move. In external circuits, it is from higher potential to lower potential.

Electron Flow

In metals, electrons drift opposite to conventional current because they are negatively charged.

Unit and Dimension

SI unit is ampere. Since I = Q/t, dimensional formula is [A].

Section 2: Mathematical Definition of Current

I = dQ/dt

Iavg = Q/t

1 A = 1 C s⁻¹

Q = It

If charge ΔQ crosses a surface in time Δt, average current is Iavg = ΔQ/Δt.

For very small time interval, instantaneous current becomes I = dQ/dt.

For steady current, equal charge crosses in equal time intervals, so I = Q/t.

Variable current changes with time; steady current remains constant.

Section 3: Flow of Electric Charges in Metallic Conductors

Metal consists of fixed positive lattice ions and mobile free electrons. Electrons undergo rapid random thermal motion. This random motion gives zero average velocity. Under electric field, electrons experience force F = -eE and acquire slow drift motion opposite to field.

electron drift ←conventional current →++++eee

Section 4: Drift Velocity

Drift velocity is the average velocity gained by free electrons due to applied electric field. It is very small because electrons repeatedly collide with lattice ions.

Force on electron: F = -eE.

Acceleration magnitude: a = eE/m.

If τ is average relaxation time between collisions, average drift speed is vd = aτ.

Therefore vd = eEτ/m.

Mean free path is average distance travelled between two collisions. Larger τ means larger mobility and drift velocity.

Section 5: Current in Terms of Drift Velocity

Consider a conductor of area A and electron density n.

In time dt, electrons in length vd dt cross the area.

Volume = Avd dt, number of electrons = nAvd dt.

Charge crossing = nAevd dt.

Current = dQ/dt = nAevd.

This formula links microscopic electron motion with macroscopic current measured by an ammeter.

Section 6: Current Density

J = I/A

J = nevd

J = σE

Unit: A m⁻²

Current density is a vector directed along conventional current. In non-uniform conductors, current may remain same in steady state while current density changes because area changes.

Section 7: Mobility of Electrons

Mobility is drift velocity per unit electric field. It measures how easily electrons drift in a material.

μ = vd/E

vd = μE

μ = eτ/m

σ = neμ

Section 8: Ohm's Law

Ohm's law states that current through a conductor is directly proportional to potential difference across it, provided temperature and physical conditions remain constant.

Macroscopic form: V = IR.

Microscopic form: J = σE.

Ohm's law is valid for ohmic conductors under constant temperature.

It fails for diodes, electrolytes, filament lamps at changing temperature and many non-linear devices.

Section 9: Resistance

Resistance is opposition offered by a conductor to current flow. It depends on length, area, material and temperature.

R = V/I

R = ρL/A

ρ = RA/L

Unit: ohm

Longer wire has more resistance; thicker wire has less resistance.

Section 10: Resistivity

Resistivity is a material property that measures intrinsic opposition to current. Conductors have low resistivity, insulators have very high resistivity, and semiconductors lie between them.

Conductors

Low resistivity, many free electrons.

Semiconductors

Moderate resistivity, strongly temperature dependent.

Insulators

Very high resistivity, almost no free charge carriers.

Section 11: Conductivity

Conductivity is reciprocal of resistivity and measures ease of current flow. Microscopically, conductivity depends on electron density and mobility.

σ = 1/ρ

σ = neμ

J = σE

Unit: S m⁻¹

Section 12: Temperature Dependence of Resistance

In metals, increasing temperature increases lattice vibrations. Electrons collide more frequently, relaxation time decreases, and resistance increases. Semiconductors usually show negative temperature coefficient because carrier concentration increases significantly with temperature.

Rt = R0(1 + αΔT)

ρt = ρ0(1 + αΔT)

Metals: α positive

Semiconductors: α negative

Metals

Resistance increases with temperature.

Carbon

Often shows negative temperature coefficient.

Thermistors

Used as temperature sensors because resistance changes strongly with temperature.

Section 13: Power and Energy

P = VI

P = I²R

P = V²/R

W = VIt

W = I²Rt

W = V²t/R

Household electricity bills are based on electrical energy consumed. One commercial unit is 1 kWh.

Section 14: Advanced Conceptual Questions

Section 15: IIT-JEE Advanced Numerical Problems

Section 16: NEET MCQs

Section 17: JEE Main MCQs

Section 18: JEE Advanced MCQs

Section 19: CBSE Case Study Questions

Section 20: Common Mistakes

Direction Confusion

Remember conventional current is opposite to electron flow in metals.

Drift Velocity Misconception

Drift velocity is small, but current can be large because number density is huge.

Mobility Mistake

Mobility is vd/E, not E/vd.

Resistivity Mistake

Resistance depends on dimensions; resistivity depends mainly on material and temperature.

Section 21: Exam Strategy

CBSE

Focus on definitions, derivations, diagrams, units and NCERT questions.

NEET

Master formulas and quick calculation traps.

JEE Main

Practise multi-step numericals and graph interpretation.

JEE Advanced

Focus on non-uniform conductors, current density vector and microscopic models.

Olympiad

Build reasoning from charge conservation and microscopic electron motion.

Still facing difficulty?

Still facing difficulty in understanding Flow of Electric Charges in Metallic Conductors, Drift Velocity, Mobility, Current Density, Resistance, Resistivity or IIT-JEE level Physics?

Contact Kumar Sir

Phone: +91-9958461445

Website: KumarPhysicsClasses.com

For personalized one-to-one Physics mentoring.