Electricity is one of the most important forms of energy, powering homes, industries, transport and communication. The study of electricity involves understanding electric charge, electric current, potential difference, resistance, and the relationships between these quantities. From the battery in a torch to the national power grid, the same fundamental laws govern the flow of electric charge. This chapter lays the foundation for understanding electrical circuits, which is essential for physics and for everyday life.
An electric current is the flow of electric charge. It flows through a conductor when there is a potential difference across its ends, maintained by a cell or battery. The resistance of a conductor opposes the flow of current, and different materials offer different amounts of resistance. Conductors like copper and aluminium have low resistance, while insulators like rubber and glass have very high resistance.
In this chapter, we will study electric current, potential difference, resistance and resistivity, Ohm's law, factors affecting resistance, the combination of resistors (series and parallel), heating effects of electric current, and electric power. Ohm's law (V = IR), the resistance laws, and the power formulae are the mathematical core of this chapter, and numerical problems based on them are frequently asked in examinations.
Electric charge is the fundamental property of matter that gives rise to electric force. The SI unit of charge is the coulomb (C). The flow of charge constitutes an electric current. The current (I) is the rate of flow of charge:
$$I = \frac{Q}{t}$$
Where Q is the charge in coulombs and t is the time in seconds. The SI unit of current is the ampere (A). One ampere is the flow of one coulomb of charge per second. By convention, the direction of current is taken as the direction of flow of positive charge, which is opposite to the direction of flow of electrons.
The electric potential at a point is the work done in bringing a unit positive charge from infinity to that point. The potential difference (V) between two points is the work done in moving a unit charge from one point to another:
$$V = \frac{W}{Q}$$
The SI unit of potential difference is the volt (V). One volt is the potential difference when one joule of work is done in moving one coulomb of charge. A cell or battery maintains the potential difference in a circuit.
Ohm's law states that the potential difference across a conductor is directly proportional to the current flowing through it, provided the physical conditions (temperature, etc.) remain constant:
$$V = IR$$
Where V is the potential difference in volts, I is the current in amperes, and R is the resistance in ohms (Ω). The resistance of a conductor is the ratio of the potential difference to the current:
$$R = \frac{V}{I}$$
A graph of V against I for a conductor obeying Ohm's law is a straight line passing through the origin. Such conductors are called ohmic conductors. Materials like semiconductors, and devices like diodes, do not obey Ohm's law and are called non-ohmic.
Resistance is the property of a conductor that opposes the flow of current. It depends on:
The resistance of a conductor is given by:
$$R = \rho \frac{l}{A}$$
Where ρ (rho) is the resistivity of the material, l is the length and A is the area of cross-section. The SI unit of resistivity is the ohm-metre (Ω m). Resistivity is a characteristic property of a material; it does not depend on the dimensions of the conductor. Good conductors like copper and silver have low resistivity, while insulators like rubber have very high resistivity.
When resistors are connected in series, the same current flows through each resistor, and the potential differences add up:
$$R_s = R_1 + R_2 + R_3 + \dots$$
When resistors are connected in parallel, the potential difference across each resistor is the same, and the total current is the sum of the currents through each resistor:
$$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$$
When an electric current flows through a conductor, the conductor heats up. This is the heating effect of electric current, caused by the collisions of the flowing electrons with the atoms of the conductor. Joule's law of heating states that the heat produced (H) in a conductor is:
$$H = I^2Rt$$
$$H = VIt = \frac{V^2}{R}t$$
Where I is the current, R is the resistance, t is the time, and V is the potential difference.
Electric power is the rate at which electrical energy is consumed or produced:
$$P = VI = I^2R = \frac{V^2}{R}$$
The SI unit of power is the watt (W). One watt is the power when one joule of energy is consumed per second. The commercial unit of electrical energy is the kilowatt-hour (kWh):
$$1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$$
The electrical energy consumed is given by:
$$E = Pt$$
Where P is the power in watts and t is the time in seconds (or hours for kWh). Electricity bills are calculated in units of kilowatt-hours.
| Quantity | Symbol | SI Unit | Formula |
|---|---|---|---|
| Electric charge | Q | Coulomb (C) | Q = It |
| Electric current | I | Ampere (A) | I = Q/t |
| Potential difference | V | Volt (V) | V = W/Q |
| Resistance | R | Ohm (Ω) | R = V/I |
| Resistivity | ρ | Ohm-metre (Ω m) | ρ = RA/l |
| Electric power | P | Watt (W) | P = VI |
| Electrical energy | E | Joule (J) | E = Pt |
| Feature | Series | Parallel |
|---|---|---|
| Current | Same through all resistors | Divides among resistors |
| Potential difference | Divides among resistors | Same across all resistors |
| Effective resistance | R1 + R2 + ... | 1/Rp = 1/R1 + 1/R2 + ... |
| Result | Total resistance increases | Total resistance decreases |
| Example | Old Christmas lights | House wiring |
Electricity is the silent force that drives the modern world, and this chapter gives you the conceptual and mathematical tools to understand it. The relationship between charge, current and potential difference, expressed through Ohm's law, is the foundation of circuit analysis. Resistance and resistivity explain why different materials and different wire dimensions conduct electricity differently, while series and parallel combinations allow circuits to be designed for specific purposes. The heating effect of electric current powers our appliances and protects our homes through the humble fuse. Electric power and energy calculations connect physics directly to our electricity bills. Mastering these formulae, understanding the circuit diagrams, and practising numerical problems will prepare you thoroughly for the board examination and give you a lasting understanding of the physics that surrounds us daily.