Electricity — Circuits and Effects

Electricity powers our lights, fans, phones, and countless machines. The flow of electricity is called electric current. Electric current is the flow of electric charge (specifically, the flow of electrons through a conductor such as a metal wire). For a current to flow, there must be a complete (closed) circuit — an unbroken path — and a source of energy such as a cell or battery to push the charges around. The SI unit of electric current is the ampere (A), and current is measured with an instrument called an ammeter.

There is a useful convention about the direction of current. Although the actual moving charges in a wire are electrons (which flow from the negative to the positive terminal), by long-standing convention the direction of conventional current is taken to be from the positive terminal to the negative terminal of the cell, through the circuit. So when we mark the direction of current in a circuit, we draw it flowing out of the positive terminal of the battery, around the circuit, and back into the negative terminal.

To make charges flow, the cell or battery provides a "push", described by the potential difference (voltage). Potential difference between two points is the work done to move a unit charge from one point to the other. It can be thought of as the "electrical pressure" that drives the current around the circuit. Potential difference is given by V = W / Q, where W is the work done (energy) and Q is the charge moved. The SI unit of potential difference is the volt (V), and it is measured with a voltmeter.

A related idea is the difference between EMF and terminal voltage. The electromotive force (EMF) of a cell is the total voltage it can provide (the energy it gives per unit charge), while the terminal voltage is the voltage actually available across its terminals when current is flowing (which is slightly less, because some energy is used up inside the cell itself). For our purposes, the key ideas are that current is the flow of charge (measured in amperes, by an ammeter), and potential difference is the push that drives it (measured in volts, by a voltmeter), given by V = W/Q. These two quantities are connected by Ohm's law, which we study next.

How is the current flowing through a conductor related to the voltage across it? This was discovered by the scientist Georg Ohm and is stated as Ohm's law. Ohm's law states that, at constant temperature, the current flowing through a conductor is directly proportional to the potential difference (voltage) across it. This means that if the voltage is doubled, the current also doubles. Ohm's law is one of the most important and useful relationships in the study of electricity.

Ohm's law is written in the simple form V = I R, where V is the potential difference (in volts), I is the current (in amperes), and R is a constant called the resistance. Resistance is the opposition that a conductor offers to the flow of electric current. A high resistance means it is harder for current to flow (so less current flows for a given voltage). The SI unit of resistance is the ohm (Ω). From Ohm's law we can find any one quantity if we know the other two: V = IR, I = V/R, and R = V/I.

If we plot a graph of voltage (V) against current (I) for a conductor that obeys Ohm's law, we get a straight line through the origin, showing that V and I are directly proportional. Such conductors are called ohmic conductors (most metals at constant temperature are ohmic). Some devices do not follow Ohm's law — their V–I graph is not a straight line — and these are called non-ohmic conductors.

The resistance of a wire depends on several factors: its length (a longer wire has more resistance), its cross-sectional area or thickness (a thicker wire has less resistance), the material it is made of, and its temperature (for most metals, resistance increases as temperature rises). The property of a material that determines its resistance is called its resistivity — a thin, long wire of a high-resistivity material has high resistance. Understanding Ohm's law (V = IR) and the factors affecting resistance lets us design and analyse electric circuits, including the series and parallel arrangements we study next.

When we connect more than one component (such as bulbs or resistors) in a circuit, they can be arranged in two main ways: in series or in parallel. The way components are connected affects how the current and voltage are shared and how the total (equivalent) resistance is worked out. Understanding series and parallel circuits is essential for designing real circuits, including those in our homes.

In a series circuit, the components are connected one after another in a single path, so the same current flows through each component (there is only one path for the current). The total voltage of the source is shared (divided) among the components. The total (equivalent) resistance of a series circuit is the sum of the individual resistances: R = R₁ + R₂ + R₃ + … This means adding more components in series increases the total resistance. A drawback of a series circuit is that if one component fails (breaks), the circuit is broken and all the components stop working (like old fairy lights where one broken bulb switched off the whole string).

In a parallel circuit, the components are connected on separate branches, so each has its own path. In a parallel circuit, the voltage across each component is the same (equal to the source voltage), while the current divides among the branches. The total resistance of a parallel circuit is found from 1/R = 1/R₁ + 1/R₂ + 1/R₃ + …, and the total (equivalent) resistance is less than the smallest individual resistance. So adding more components in parallel actually decreases the total resistance and increases the total current drawn.

Parallel circuits have important advantages over series circuits for household wiring. Because each branch is independent, if one component fails, the others keep working (one bulb going out does not switch off the rest). Also, each component gets the full voltage, so all appliances work at their proper voltage, and each can be switched on and off separately. For these reasons, the electrical appliances in our homes are connected in parallel. Knowing the rules for series circuits (same current, resistances add) and parallel circuits (same voltage, total resistance decreases) lets us understand and design practical electric circuits.

When electric current flows through an appliance, it does work and uses energy. The rate at which this happens is described by electric power. Electric power is the rate at which electrical energy is used (or work is done) — that is, the energy used per second. A high-power appliance uses energy quickly. The SI unit of power is the watt (W), where 1 watt means 1 joule of energy used per second. Larger powers are measured in kilowatts (kW), where 1 kW = 1000 W.

Electric power can be calculated in several equivalent ways. The basic formula is P = V I (power = voltage × current). Using Ohm's law (V = IR), this can also be written as P = I² R and P = V² / R. These three forms — P = VI = I²R = V²/R — all give the power and are used depending on which quantities are known. For example, a bulb rated "60 W, 230 V" uses 60 joules of electrical energy every second when connected to 230 V.

To work out the electrical energy used (which is what we pay for), we multiply the power by the time for which it is used: Energy = Power × Time. If power is in watts and time in seconds, energy is in joules. But for household use, energy is measured in a larger, more convenient unit: the kilowatt-hour (kWh), also called 1 unit of electricity. One kilowatt-hour is the energy used by a 1 kW appliance in 1 hour. So energy (in kWh) = power (in kW) × time (in hours).

This is the basis of household electricity billing. The electricity meter in a house records the total energy used in kilowatt-hours (units), and the bill is calculated by multiplying the number of units used by the cost per unit. For example, a 2 kW heater used for 3 hours consumes 2 × 3 = 6 kWh (6 units) of energy. By knowing the power ratings of appliances and how long they are used, we can calculate energy consumption and electricity bills — and by using efficient appliances and switching them off when not needed, we can save energy and money. Understanding electric power (P = VI = I²R = V²/R) and energy (in kWh) connects the physics of circuits to everyday life.

When an electric current flows through a wire that has resistance, the wire becomes hot. This production of heat when current flows through a resistance is called the heating effect of electric current, also known as Joule's heating. It happens because the moving charges collide with the particles of the conductor, giving up energy as heat. The amount of heat produced is given by H = I² R t, where H is the heat, I is the current, R is the resistance, and t is the time. So more current, more resistance, and more time all produce more heat.

The heating effect has many useful applications. Appliances designed to produce heat use a coil of high-resistance wire that gets hot when current flows: electric heaters, irons, geysers, toasters, and electric kettles all work this way. The filament of an incandescent bulb is a thin, high-resistance wire that gets so hot it glows and gives light. An important protective device based on the heating effect is the fuse — a short piece of wire with a low melting point placed in a circuit; if too large a current flows (as in a fault), the fuse wire heats up and melts, breaking the circuit and protecting the appliances and wiring from damage or fire.

In our homes, electricity is supplied through domestic electric circuits using three wires: the live wire (which carries the current at high voltage), the neutral wire (which completes the circuit), and the earth wire (a safety wire connected to the ground). Appliances are connected in parallel between the live and neutral wires, so each gets the full voltage and can be operated independently. Switches are always placed in the live wire so that, when switched off, the appliance is fully disconnected from the dangerous live supply.

Several safety devices protect domestic circuits. The fuse (or a modern MCB — Miniature Circuit Breaker, which switches off automatically instead of melting) protects against excessive current from short circuits or overloading. Earthing — connecting the metal body of an appliance to the earth wire — is a vital safety measure: if a fault makes the metal body live, the earth wire carries the current safely to the ground, preventing electric shocks. A short circuit (when the live and neutral wires touch directly) causes a sudden large current and is dangerous; the fuse or MCB cuts off the supply to prevent fire. By understanding the heating effect and the design and safety devices of domestic circuits, we can use electricity both effectively and safely, completing our study of electricity.