Welcome to Electricity!
Electricity is all around us. From charging your smartphone to powering the lights in your home and running massive hospital machines, electricity plays a central role in modern life. In this chapter, we will break down the invisible world of electric charges, circuits, and energy into simple, bite-sized ideas.
Don't worry if physics equations sometimes seem daunting! We will take everything step-by-step with clear analogies, real-world examples, and helpful memory tricks.
---1. Electric Charge and Current
What is Electric Charge?
Everything in the universe is made of atoms, which contain tiny charged particles. Electrons carry a negative charge, while protons carry a positive charge. In metals (like copper wires), some electrons are free to move between atoms. These are called free electrons or delocalised electrons.
Electric charge is given the symbol \(Q\) and is measured in coulombs (\(\text{C}\)). One coulomb is a huge bundle of charge containing roughly \(6.25 \times 10^{18}\) electrons!
What is Electric Current?
Electric current is the rate of flow of electric charge around a circuit. When electrons move through a wire, an electric current is flowing.
Analogy: Think of a central heating system. Water flowing through the pipes is like electric charge flowing through wires. The faster the water flows past a point, the higher the flow rate. In a wire, the more charge that passes a point each second, the larger the electric current.
The Current Equation
We calculate current using the formula:
\(Q = I \times t\)
Where:
• \(Q\) = Electric charge measured in coulombs (\(\text{C}\))
• \(I\) = Electric current measured in amperes or amps (\(\text{A}\))
• \(t\) = Time measured in seconds (\(\text{s}\))
You can also rearrange this formula to find current or time:
• \(I = \frac{Q}{t}\)
• \(t = \frac{Q}{I}\)
Example: A current of \(0.5\text{ A}\) flows through a lamp for \(2\text{ minutes}\). How much charge passes through the lamp?
Step 1: Convert time into seconds: \(t = 2 \times 60 = 120\text{ s}\).
Step 2: Use \(Q = I \times t\).
Step 3: Calculate: \(Q = 0.5\text{ A} \times 120\text{ s} = 60\text{ C}\).
Measuring Current
• Current is measured using an ammeter.
• An ammeter must always be connected in series (in the same loop) with the component you want to measure.
• An ideal ammeter has nearly zero resistance so it does not slow down the flow of current.
Key Takeaway: Electric current (\(I\)) is the rate of flow of charge (\(Q\)) over time (\(t\)). Always convert time to seconds before calculating!
---2. Potential Difference (Voltage)
What is Potential Difference?
For electrons to move through a circuit, something needs to push them. A battery or power supply provides this "push". The scientific name for this electrical push is potential difference (often called voltage).
Potential difference (p.d.) is defined as the energy transferred per unit of charge between two points in a circuit.
The Voltage Equation
\(V = \frac{W}{Q}\) or \(W = Q \times V\)
Where:
• \(V\) = Potential difference (voltage) in volts (\(\text{V}\))
• \(W\) = Energy transferred (or work done) in joules (\(\text{J}\))
• \(Q\) = Charge in coulombs (\(\text{C}\))
Did you know? \(1\text{ volt}\) is equal to \(1\text{ joule of energy per coulomb of charge}\) (\(1\text{ V} = 1\text{ J/C}\)). If a battery has a rating of \(12\text{ V}\), it gives \(12\text{ J}\) of energy to every single coulomb of charge passing through it.
Measuring Potential Difference
• Voltage is measured using a voltmeter.
• A voltmeter must always be connected in parallel across (around) the component you are testing.
• An ideal voltmeter has very high resistance so that no current bypasses the component through the meter.
Common Mistake to Avoid: Never connect a voltmeter in series or an ammeter in parallel. Remember: Ammeter in a line (series), Voltmeter around the component (parallel).
---3. Resistance and Ohm's Law
What is Resistance?
As electrons flow through a metal wire, they collide with the vibrating positive ions in the metal lattice. These collisions slow the electrons down and transfer energy as heat. This opposition to the flow of current is called resistance.
• The higher the resistance of a component, the lower the current that flows for a given voltage.
• Resistance is measured in ohms (\(\Omega\)).
Ohm's Law
Ohm's Law states: The current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature remains constant.
The mathematical relationship is:
\(V = I \times R\)
Where:
• \(V\) = Potential difference in volts (\(\text{V}\))
• \(I\) = Current in amperes (\(\text{A}\))
• \(R\) = Resistance in ohms (\(\Omega\))
Rearranged forms:
• \(R = \frac{V}{I}\)
• \(I = \frac{V}{R}\)
Investigating Current-Voltage (I-V) Characteristics
Different components respond differently when voltage changes:
1. Fixed Resistor (Ohmic Conductor at constant temperature):
• The graph of current against voltage (\(I-V\)) is a straight line passing through the origin (\(0,0\)).
• This shows that current is directly proportional to voltage. The resistance is constant.
2. Filament Lamp (Non-Ohmic):
• The \(I-V\) graph is an S-shaped curve that flattens at higher voltages.
• Why? As current increases, the thin filament wire gets hotter. The metal ions vibrate faster and collide more frequently with passing electrons. This causes the resistance to increase, bending the curve.
3. Semiconductor Diode:
• A diode allows current to flow in only one direction (forward bias).
• In the forward direction, current only begins to flow after a small threshold voltage (around \(0.6\text{ V}\)), after which resistance drops sharply.
• In the reverse direction (reverse bias), it has extremely high resistance, and virtually zero current flows.
4. Thermistor (Temperature-dependent Resistor):
• As temperature increases, its resistance decreases.
• Memory trick: Thermistor = Turbo hot, Low resistance. Useful in digital thermometers, thermostats, and fire alarms.
5. Light Dependent Resistor (LDR):
• As light intensity increases, its resistance decreases.
• Memory trick: Light Up \(\rightarrow\) Resistance Down (LURD). Useful in automatic street lights and solar-powered garden lamps.
Key Takeaway: Resistance opposes current (\(R = \frac{V}{I}\)). For fixed resistors, resistance is constant. For filament lamps, resistance increases as temperature rises. For thermistors and LDRs, resistance drops as heat or light increases.
---4. Series and Parallel Circuits
Series Circuits
In a series circuit, all components are connected one after another in a single continuous loop.
• Current: Current is the same everywhere at every point.
\(I_{\text{total}} = I_1 = I_2 = I_3\)
• Voltage: The total voltage from the power source is shared between the components.
\(V_{\text{total}} = V_1 + V_2 + V_3\)
• Total Resistance: The total resistance is simply the sum of all individual resistances.
\(R_{\text{total}} = R_1 + R_2 + R_3\)
Example: Two resistors of \(4\ \Omega\) and \(6\ \Omega\) are connected in series with a \(20\text{ V}\) battery.
• Total resistance: \(R_{\text{total}} = 4\ \Omega + 6\ \Omega = 10\ \Omega\).
• Current in circuit: \(I = \frac{V}{R_{\text{total}}} = \frac{20\text{ V}}{10\ \Omega} = 2\text{ A}\).
• Voltage across the \(4\ \Omega\) resistor: \(V_1 = I \times R_1 = 2\text{ A} \times 4\ \Omega = 8\text{ V}\).
• Voltage across the \(6\ \Omega\) resistor: \(V_2 = I \times R_2 = 2\text{ A} \times 6\ \Omega = 12\text{ V}\).
Notice: \(8\text{ V} + 12\text{ V} = 20\text{ V}\), which matches the battery voltage!
Parallel Circuits
In a parallel circuit, the circuit splits into two or more separate branches.
• Voltage: The potential difference across each branch is the same as the supply voltage.
\(V_{\text{supply}} = V_1 = V_2\)
• Current: The total current leaving the supply is shared among the branches.
\(I_{\text{total}} = I_1 + I_2 + I_3\)
• Total Resistance: Adding resistors in parallel reduces the overall resistance because it provides additional pathways for current to flow. The total resistance of resistors in parallel is always less than the resistance of the smallest individual resistor.
Why are homes wired in parallel?
1. Each appliance receives the full mains voltage (\(230\text{ V}\)).
2. Each appliance can be switched on or off independently.
3. If one light bulb blows, the other lights stay on.
5. Electrical Power and Energy
What is Electrical Power?
Power is the rate at which electrical energy is transferred or work is done. It is measured in watts (\(\text{W}\)), where \(1\text{ watt} = 1\text{ joule per second}\) (\(1\text{ W} = 1\text{ J/s}\)).
Power Formulas
Depending on the values you are given in an exam, use one of these three formulas:
1. \(P = I \times V\)
2. \(P = I^2 \times R\)
3. \(P = \frac{V^2}{R}\)
Where:
• \(P\) = Power in watts (\(\text{W}\))
• \(I\) = Current in amperes (\(\text{A}\))
• \(V\) = Potential difference in volts (\(\text{V}\))
• \(R\) = Resistance in ohms (\(\Omega\))
Calculating Electrical Energy
The energy transferred by an appliance depends on its power and how long it is turned on:
\(E = P \times t\)
Substituting \(P = I \times V\) gives:
\(E = I \times V \times t\)
Where:
• \(E\) = Energy in joules (\(\text{J}\))
• \(P\) = Power in watts (\(\text{W}\))
• \(t\) = Time in seconds (\(\text{s}\))
Costing Domestic Electricity (Kilowatt-hours)
Because a joule is a very small amount of energy, electricity companies measure household energy consumption in kilowatt-hours (\(\text{kWh}\)), often called units of electricity.
• \(1\text{ kilowatt-hour (kWh)}\) is the electrical energy consumed by a \(1\text{ kW}\) (\(1000\text{ W}\)) appliance running for \(1\text{ hour}\).
Formulas for Electricity Cost:
\(\text{Units used (kWh)} = \text{Power in kW} \times \text{Time in hours}\)
\(\text{Total Cost} = \text{Units used (kWh)} \times \text{Cost per unit (in pence or \pounds)}\)
Example: An electric heater with a power rating of \(2\text{ kW}\) is used for \(3.5\text{ hours}\). Electricity costs \(28\text{p}\) per unit. How much does it cost to run the heater?
Step 1: Calculate energy in \(\text{kWh}\): \(\text{Energy} = 2\text{ kW} \times 3.5\text{ h} = 7\text{ kWh}\).
Step 2: Calculate total cost: \(\text{Cost} = 7\text{ units} \times 28\text{p} = 196\text{p} = \text{\pounds}1.96\).
Key Takeaway: For calculations in Joules, use Watts and seconds. For calculations in kWh (cost), use Kilowatts and hours.
---6. Domestic Electricity and Safety
Direct Current (d.c.) vs Alternating Current (a.c.)
• Direct Current (d.c.): The current flows in one direction only. Cells and batteries supply direct current.
• Alternating Current (a.c.): The direction of current flow constantly reverses back and forth. Mains electricity supplied to our homes is alternating current.
• UK Mains Supply Values: The UK mains electricity has a voltage of \(230\text{ V}\) and a frequency of \(50\text{ Hz}\) (it changes direction \(50\) times per second).
The Three-Pin Plug
Mains appliances are connected using a three-pin plug containing three insulated copper wires:
1. Live Wire (Brown):
• Carries the high alternating voltage (\(230\text{ V}\)) from the supply to the appliance.
• Memory aid: Brown goes to the Bottom Right.
2. Neutral Wire (Blue):
• Completes the circuit, carrying current away from the appliance back to the source at near \(0\text{ V}\).
• Memory aid: Blue goes to the Bottom Left.
3. Earth Wire (Green and Yellow Stripes):
• A safety wire connected to the metal casing of an appliance and into the ground. It is at \(0\text{ V}\).
• Memory aid: Striped goes to the Top pin.
Electrical Safety Devices
1. The Fuse:
• A fuse contains a thin wire with a low melting point placed in the live wire.
• If an electrical fault causes an excessive current to flow, the thin wire heats up, melts ("blows"), and breaks the circuit. This prevents the appliance from overheating and causing an electrical fire.
• Fuse Rating: Common fuses are rated at \(3\text{ A}\), \(5\text{ A}\), and \(13\text{ A}\). A fuse rating should always be just slightly higher than the normal operating current of the device.
2. Earthing:
• If a live wire comes loose inside an appliance and touches the metal casing, anyone touching the appliance could receive a dangerous electric shock.
• The earth wire provides a very low-resistance path from the metal case straight into the ground.
• A huge surge of current rushes safely down the earth wire, which immediately melts the fuse and cuts off the power.
3. Circuit Breakers (MCBs and RCCBs):
• Modern consumer units use electromagnetic switches called Miniature Circuit Breakers (MCBs) and Residual Current Circuit Breakers (RCCBs) instead of fuses.
• Advantages over fuses: They operate much faster than fuses and can easily be reset by flipping a switch (no need to replace a melted wire).
4. Double Insulation:
• Some appliances (like hair dryers and electric drills) have an outer casing made entirely of plastic (an electrical insulator).
• Because the user cannot touch any metal parts even if a wire comes loose, these appliances do not require an earth wire. They only have a live wire and a neutral wire.
Quick Formula Summary Table
• Charge and Current: \(Q = I \times t\)
• Voltage and Energy: \(V = \frac{W}{Q}\)
• Ohm's Law: \(V = I \times R\)
• Series Resistance: \(R_{\text{total}} = R_1 + R_2 + ...\)
• Electrical Power: \(P = I \times V\) | \(P = I^2 \times R\) | \(P = \frac{V^2}{R}\)
• Electrical Energy: \(E = P \times t\) | \(E = I \times V \times t\)
• Domestic Electricity Cost: \(\text{Cost} = \text{Power (kW)} \times \text{Time (hours)} \times \text{Cost per unit}\)