Electric Current and Potential Difference

Electric current is defined as the rate of flow of electric charge through a cross-section of a conductor. It represents the ordered motion of charge carriers under the influence of an external electric field.

Charge Carriers in Different Media

• Solid Conductors (Metals): The charge carriers are free electrons. The atomic nuclei remain fixed within the crystalline lattice.
• Electrolytes: The charge carriers are both positive ions (cations) and negative ions (anions) moving in opposite directions.
• Gases: The charge carriers are positive ions and free electrons, typically created under high voltage or low-pressure ionization.

Mathematical Representation and Units

If a net charge Q passes through any cross-section of a conductor in time t, the average electric current I is given by:

For a variable flow of charge, the instantaneous current is expressed as:

• SI Unit: The SI unit of electric current is the Ampere (A). One Ampere is defined as the flow of one Coulomb of charge per second (1 A = 1 C/s).
• Scalar Nature: Even though electric current has a specific direction, it is a scalar quantity. This is because it obeys the laws of ordinary algebra rather than vector algebra; for instance, when two currents meet at a junction, the resultant current is simply their algebraic sum.

Direction of Electric Current

• Conventional Current: Historically, the direction of current was assumed to be the direction of the flow of positive charges. Therefore, conventional current flows from the positive terminal to the negative terminal of a power source.
• Electronic Current: The actual flow of electrons in a metallic conductor is from the negative terminal to the positive terminal. Conventional current is always opposite to the direction of electron flow.

Electric Potential and Potential Difference

Electric potential and potential difference are the driving forces that cause electric charges to move through a circuit, analogous to pressure differences causing fluid flow.

Electric Potential (V)

Electric potential at a point in an electric field is defined as the amount of work done in bringing a unit positive test charge from infinity to that point against the electrostatic forces.

Electric Potential Difference (Δ V)

Potential difference between two points in an electrical circuit is the work done per unit charge in moving a positive test charge from one point to another.

Where W_AB is the work done in moving charge q from point A to point B.

• SI Unit: The SI unit of potential difference is the Volt (V). One Volt is equal to one Joule per Coulomb (1 V = 1 J/C).
• Physical Analogy: It represents electrical pressure. Charge naturally flows from a region of higher electric potential to a region of lower electric potential.

Electromotive Force (EMF) vs. Potential Difference

While both are measured in Volts, they represent distinct thermodynamic conditions in a circuit.

Parameter	Electromotive Force (EMF)	Potential Difference (Terminal Voltage)
Definition	The maximum potential difference between the electrodes of a cell when no current is drawn (Open Circuit).	The potential difference between two points or terminals when the circuit is switched on (Closed Circuit).
Cause/Effect	It is the cause. It represents the energy supplied by the source.	It is the effect. It represents the energy dissipated across a component.
Internal Resistance	Independent of the internal resistance of the cell.	Decreases as the internal resistance of the cell increases during current flow.
Magnitude	Always greater than the potential difference across the circuit during discharge.	Always less than the EMF of the cell when current is being drawn.

Ohm’s Law and Electrical Resistance

Ohm’s Law establishes the linear relationship between electric current and potential difference for metallic conductors at a constant temperature.

Statement of Ohm’s Law

The electric current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across its ends, provided physical conditions such as temperature, mechanical strain, and material composition remain constant.

Where R is a constant called the Electrical Resistance of the conductor.

Electrical Resistance (R)

Resistance is the inherent property of a material to oppose the flow of electric current through it. It arises due to frequent collisions of drifting electrons with the constituent atoms or ions of the conductor.

• SI Unit: The SI unit of resistance is the Ohm (Ω). 1 Ω = 1 V/A.
• Factors Affecting Resistance:
  1. Length (l): Resistance is directly proportional to the length of the conductor (R ∝ l).
  2. Area of Cross-Section (A): Resistance is inversely proportional to the cross-sectional area (R ∝ 1/A).
  3. Nature of Material: Characterized by the intrinsic property called resistivity.
  4. Temperature: For pure metals, resistance increases with an increase in temperature due to increased thermal vibrations of the lattice ions, which impede electron drift.

Electrical Resistivity (ρ)

Combining the structural factors, resistance is written as:

Where ρ (rho) is the Electrical Resistivity (or specific resistance) of the material.

• SI Unit: Ohm-meter (Ω·m).
• Distinction: Resistivity is an intrinsic property of the material. It depends only on the nature of the material and its temperature; it does not depend on the dimensions (length or area) of the conductor.

Drift Velocity and the Mechanism of Conduction

In the absence of any external potential difference, free electrons in a metal move randomly due to thermal energy (with speeds up to 10⁵ m/s), resulting in a net zero current in any specific direction.

Mechanism under an Electric Field

When a potential difference is applied across the conductor, an internal electric field (E) is established. This field exerts an electrostatic force on the free electrons, causing them to accelerate toward the positive terminal. However, due to continuous collisions with the fixed positive ions of the lattice, the electrons acquire a steady, slow net average velocity.

Drift Velocity (v_d)

Drift velocity is the average velocity acquired by free electrons in a conductor under the influence of an external electric field.

Where e is electronic charge, E is electric field intensity, m is mass of an electron, and τ (tau) is the average relaxation time (the mean time interval between two successive collisions).

• Magnitude: The drift velocity is surprisingly small, typically on the order of 10^-4 m/s (0.1 mm/s).
• UPSC Prelims Pointer: Despite the extremely slow drift velocity of electrons, an electrical appliance turns on instantaneously when the switch is flipped. This is because the electric field travels through the conductor at nearly the speed of light (≈ 3 × 10⁸ m/s), initiating drift among all free electrons throughout the entire circuit simultaneously.

Classification of Materials based on Electrical Conductivity

Category	Characteristic	Resistivity Range (Ω⋅m)	Temperature Effect on Resistance	Examples
Conductors	Large number of free electrons; low resistance.	10-8 to 10-6	Resistance increases with temperature.	Copper, Silver, Aluminum, Iron.
Insulators	No free electrons available for conduction.	1012 to 1019	Negligible change (remains highly resistive).	Glass, Rubber, Wood, Plastic.
Semiconductors	Intermediate conductivity; behaves as insulators at 0 K.	10-5 to 105	Resistance decreases with temperature.	Silicon, Germanium.
Superconductors	Zero electrical resistance below a critical temperature.	$0$	Drops abruptly to zero at critical temperature (Tc).	Mercury (below 4.2 K), Lead (below 7.2 K).

Core Electrical Measuring Instruments

Ammeter

• Function: Measures the magnitude of electric current flowing through a circuit branch.
• Connection: Always connected in series with the component whose current is to be measured.
• Ideal Condition: An ideal ammeter has zero resistance so that its insertion does not alter the actual current flowing through the circuit.

Voltmeter

• Function: Measures the electric potential difference between two specific points in a circuit.
• Connection: Always connected in parallel across the component whose voltage drop is to be measured.
• Ideal Condition: An ideal voltmeter has infinite resistance so that it draws no current from the main circuit branch.

Galvanometer

• Function: A sensitive electromechanical instrument used to detect the presence, direction, and small magnitudes of electric current. It can be modified into an ammeter (by connecting a low resistance shunt in parallel) or into a voltmeter (by connecting a high resistance in series).

Last Modified: May 28, 2026