Notes Electric Current & Circuits - Science & Pedagogy Paper 2 for CTET & TET Exams

Electric Current

Electric current is the rate at which electric charge flows through a conductor. It is associated with charges in motion and therefore belongs to dynamic electricity. Current is represented by the symbol I.

• Mathematical definition: I = q / t, where q is the electric charge that flows and t is the time taken.
• S.I. unit: ampere (A). A smaller commonly used unit is the milliampere (mA) where 1 mA = 10−3 A.
• Measurement: Electric current is measured by an ammeter.

Conventional and Electron Flow

• Conventional current is taken as the flow of positive charge and is considered from the positive terminal to the negative terminal of a cell in an external circuit.
• Actual charge carriers in a metallic conductor are electrons, which flow from the negative terminal to the positive terminal; this is opposite to conventional current direction.

Types of Current

• Direct Current (DC): Current that flows in one direction only and has zero frequency. Examples: current from a cell, DC supply for small electronics.
• Alternating Current (AC): Current whose magnitude and direction change periodically with time. Household electricity is supplied as AC with a frequency of 50 Hz in many countries.

Electric Circuit

• Electric circuit: A complete path through which electric current can flow is called an electric circuit.
• If the terminals of a bulb are connected to the terminals of an electric cell by conducting wires, current passes through the filament and the bulb glows.
• Circuit components: Common components are cells (or batteries), wires, resistors, switches, bulbs, ammeters and voltmeters.

Electricity (Static and Dynamic)

• Electricity is a form of energy related to electric charges. When charges are at rest the phenomenon is called static electricity. When charges are in motion it is called dynamic electricity.

Electric Charges and Their Properties

William Gilbert was among the early scientists who studied electric effects produced by rubbing certain materials and described the property of attracting light bodies. A body that acquires this property is said to be charged.

• Types of charge: Positive and negative.
• Interaction: Opposite charges attract each other and like charges repel each other.
• Quantisation: Electric charge occurs in discrete amounts (integral multiples of the elementary charge).
• S.I. unit of charge: coulomb (C). One coulomb corresponds to approximately 6.25 × 10¹⁸ electrons (since the magnitude of charge of one electron is about 1.6 × 10⁻¹⁹ C).

Coulomb's Law

Coulomb's law gives the magnitude of the electrostatic force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

• Mathematical form: F = k (q₁ q₂) / r², where F is the electrostatic force, q₁ and q₂ are the charges, r is the distance between them and k is the proportionality constant.
• Direction: The force acts along the line joining the two charges; it is attractive for opposite signs and repulsive for like signs.

Electric Conductors, Insulators and Semiconductors

• Conductors: Materials which allow electric current to pass through them easily because they have large numbers of free electrons. Examples: copper, aluminium, iron.
• Insulators: Materials which do not allow free movement of charge and so do not conduct current. Examples: plastic, wood, glass.
• Semiconductors: Materials whose conductivity is intermediate and can be changed by impurities, temperature or light. Examples: silicon, germanium.

Electric Cell and Battery

• Electric cell: A device that converts chemical energy into electrical energy and has two terminals, positive (+) and negative (−). It provides a potential difference between its terminals.
• Battery: A combination of two or more cells connected together to provide greater voltage or current capacity. Examples: dry cell batteries used in torches and remote controls.
• When a cell is exhausted: If the chemicals inside are used up, the cell stops supplying current.

Electric Potential and Potential Difference

• Electric potential (V): The work done in bringing a unit positive charge from infinity to a point in an electric field. Its S.I. unit is the volt (V).
• Potential difference (ΔV): The work done to move a charge from one point to another in an electric field divided by the magnitude of the charge. A potential difference is necessary to produce a steady current through a conductor.

Ohm's Law and Resistance

Ohm's law states that the current flowing through a conductor is directly proportional to the potential difference across its ends, provided physical conditions such as temperature remain constant.

• Mathematical form: V = I R, where V is the potential difference, I is the current and R is the resistance.
• Limitations: Ohm's law holds for many conductors (called ohmic conductors) for which resistance stays constant with voltage. Some devices (e.g., diodes, filament lamps) are non‐ohmic and do not follow Ohm's law over wide ranges.

Resistance

• Definition: Resistance is the property of a substance that resists the flow of electric current through it.
• Unit: ohm (Ω).
• Typical behaviour: Conductors like copper and silver have low resistance while insulators like glass and wood have very high resistance.

Factors Affecting Resistance

• Length (L): Resistance is directly proportional to the length of the conductor. If length increases, resistance increases.
• Cross‐sectional area (A): Resistance is inversely proportional to the area of cross‐section. A thicker wire has less resistance.
• Material (resistivity ρ): Resistance depends on the nature of the material; different materials have different intrinsic resistivities.

Mathematically, the resistance of a uniform conductor is given by R = ρ L / A, where ρ (rho) is the resistivity of the material. The S.I. unit of resistivity is ohm metre (Ω·m).

Series and Parallel Combination of Resistances

• Series combination: Resistors connected end to end carry the same current. Equivalent resistance is R_eq = R₁ + R₂ + ....
• Parallel combination: Resistors connected side by side have the same potential difference across them. Equivalent resistance is 1 / R_eq = 1 / R₁ + 1 / R₂ + ....
• Useful point: In series, R increases; in parallel, R decreases (and R_eq is always less than the smallest branch resistance).

Measuring Instruments: Ammeter and Voltmeter

• Ammeter: Measures current. It must be connected in series with the circuit element whose current is to be measured. An ideal ammeter has zero resistance.
• Voltmeter: Measures potential difference between two points. It must be connected in parallel with the element across which the voltage is measured. An ideal voltmeter has infinite resistance.

Heating Effect of Current and Electrical Power

• Power delivered by an electrical device: P = V I, where P is power in watts, V is potential difference and I is current.
• Using Ohm's law, power can be written as P = I² R or P = V² / R.
• Joule's law of heating: Heat produced in a resistor in time t is H = I² R t.
• Applications: Electric heaters, electric bulbs, fuses and toasters use the heating effect of current.

Simple Numerical Examples

Example 1

Problem: If a charge of 0.5 C passes through a wire in 2 s, what is the current?

Sol.

I = q / t

I = 0.5 C ÷ 2 s

I = 0.25 A

Example 2

Problem: A resistor of resistance 8 Ω carries a current of 0.5 A. Find the potential difference across it and the power dissipated.

Sol.

Use V = I R

V = 0.5 A × 8 Ω

V = 4 V

Use P = I² R

P = (0.5 A)² × 8 Ω

P = 0.25 × 8 W

P = 2 W

Applications and Classroom Teaching Notes

• Use simple circuit kits to demonstrate series and parallel connections and the effect on bulb brightness to make resistance concepts tangible.
• Demonstrate Ohm's law with a metallic wire at nearly constant temperature; show non‐ohmic behaviour using a filament lamp or diode.
• Relate household safety to the heating effect: fuses and earthing protect against excessive current and heating.
• Introduce basic calculations that combine V = IR and P = VI in exercises so that learners become comfortable switching between formulae.

Summary

Electric current measures the flow of charge and is central to dynamic electricity. Key concepts include the distinction between DC and AC, the need for a complete circuit, Coulomb's law for forces between charges, Ohm's law for current-voltage relations, the dependence of resistance on length, area and material, and practical results such as power dissipation and heating. Understanding how to measure current and potential difference with ammeters and voltmeters and how resistors combine in series and parallel is important for solving circuit problems and for practical electrical safety and devices.