CP9 · Electricity and circuitsTopic 10 — Electricity and circuits
Current, voltage, resistance, circuit rules, electrical power and mains safety.
Revise the key ideas
Charge, current and potential difference
Atoms contain positive protons, neutral neutrons and negative electrons. Metals have mobile delocalised electrons, allowing charge to move through a circuit.
A complete conducting loop and potential difference are needed for a steady current. Opening a switch breaks the circuit; an insulator prevents free charge flow.
Conventional current travels from the positive supply terminal to the negative through the external circuit. Electrons in metal drift in the opposite direction; show conventional current unless asked otherwise.
Current is the rate of charge flow: I = Q/t or Q = It. Current is in amperes (A), charge in coulombs (C) and time in seconds (s).
An ammeter measures current and is connected in series with the component. It has very low resistance; do not put it directly across a supply.
Potential difference (voltage) is the energy transferred for each coulomb of charge passing through a component: V = E/Q or E = QV. It is measured in volts (V); 1 V = 1 J/C.
A voltmeter measures potential difference and is connected in parallel across a component. It has high resistance so draws little current.A is in the current path; V spans the resistor.
Charge is conserved: current is not “used up” by a lamp. The charges transfer energy as they pass through components.
Use standard circuit symbols for cells, batteries, lamps, switches, resistors, diodes, ammeters and voltmeters. A longer cell line is the positive terminal.Longer cell line denotes positive; a battery has multiple cells.
Series and parallel circuits
A series circuit has one route for current; the same current passes through every component. Breaking any part stops the whole loop.
In series, supply voltage equals the sum of voltages across components. Equal components may share equally; different components need not.
Series resistances add: R_total = R₁ + R₂ + …. Adding a resistor at fixed supply voltage decreases current.
A parallel circuit has branches joined at junctions. Total current into a junction equals total current out; it splits between branches and rejoins.Parallel branches share the same supply voltage.
Each branch connected across the supply has the same potential difference as the supply. Components within one branch can still share that voltage in series.
With a fixed supply voltage, adding a parallel branch increases total current and decreases total circuit resistance. It provides an extra conducting route.
A failed lamp in one parallel branch need not stop current in the other branches. Household appliances are connected in parallel so each receives the supply voltage independently.
Resistance and component behaviour
Resistance relates voltage to current: V = IR and R = V/I. Resistance is measured in ohms (Ω). Use the voltage and current for the same component.
An ohmic resistor obeys Ohm’s law: at constant temperature, current is directly proportional to voltage. Doubling voltage doubles current. Its current–voltage graph is a straight line through the origin.A linear I–V relation corresponds to constant resistance.
Resistance of a metal wire generally increases with length and decreases with cross-sectional area. Material and temperature also affect it.
Heating a metal makes its ions vibrate more strongly. Moving electrons collide more with this vibrating lattice, so resistance increases. Current then rises less quickly as voltage increases.
A filament lamp's current–voltage graph curves as its filament heats. Current continues to increase with voltage; it does not suddenly become constant. Its resistance increases at higher temperature.At higher voltage, current rises less steeply; it does not become fixed.
A diode lets current flow mainly in one direction (the forward direction), once the voltage is high enough. In the reverse direction, the current is very small under normal operating conditions.The precise forward-voltage region depends on the diode.
An LDR's resistance decreases as light intensity increases. It can be used in a light-sensitive circuit.
A typical NTC thermistor's resistance decreases as temperature increases. State the type: not every thermistor behaves this way.
Investigating circuits: core practical
Use a low-voltage supply, switch, ammeter in series and voltmeter across the test component. A variable resistor or adjustable supply changes the potential difference.
For a resistor, filament lamp and diode, record paired current and voltage readings over a suitable range. Reverse supply polarity to investigate negative voltage/current where appropriate.
Plot current on the vertical axis and voltage on the horizontal axis. A resistor gives a straight line, a filament lamp gives a curve, and a diode conducts mainly in one direction.
To investigate wire resistance, measure a known length between contacts and use R = V/I. Vary length while keeping wire material, thickness and temperature as constant as possible.
Use low currents and switch off between readings to limit unwanted heating. Keep connections secure, repeat readings and use suitable meter ranges.
Do not infer resistance from an arbitrary tangent gradient of a non-ohmic I–V graph: the resistance at an operating point is V/I there.
Electrical heating, energy and power
Moving charges transfer energy to the vibrating ions in a resistive component, heating it. This is useful in heaters and kettles, but can be unwanted in cables and chargers.
Energy transferred = voltage × current × time, E = VIt, in J with V, A and s. This follows from E = QV and Q = It.
Power = energy/time, P = E/t. Electrical power also equals IV, and for a resistive component P = I²R. Power is measured in watts (W).
A 12 V device carrying 2 A has power 24 W and transfers 240 J in 10 s. A power rating tells you energy transferred each second, not total energy already used.
A higher resistance does not always mean a greater heating power: at fixed current P = I²R rises with R; at fixed voltage P = V²/R falls with R.
Reduce cable heating with appropriate low-resistance material and sufficiently thick wire. Do not treat a dangerously hot cable as normal useful heating.
Direct and alternating current
Cells and batteries supply direct current: charge moves in one direction around the external circuit. DC voltage has fixed polarity.
Alternating current reverses direction repeatedly as the supply voltage changes polarity. The UK mains supply is about 230 V and 50 Hz.
A frequency of 50 Hz means 50 complete cycles each second; a sinusoidal current reverses direction twice per cycle. One cycle lasts 0.02 s.50 Hz means 50 cycles per second, not 50 reversals per second.
Large domestic appliances use mains electricity; their energy is supplied by a network of generators and transmission/distribution lines. Battery devices instead draw from stored chemical energy.
Mains wiring and protection
In a three-core cable, live is brown, neutral is blue and earth is green-and-yellow. Live is at about 230 V relative to earth; neutral is close to earth potential, about 0 V.
The live wire supplies alternating potential difference; neutral completes the normal circuit. The earth wire is a protective connection to exposed metal casing, normally carrying no current.
If live touches an earthed metal case, the low-resistance earth path allows a large fault current, causing a fuse or suitable circuit breaker to disconnect the supply.The earth connection helps protective disconnection; it does not replace safe wiring.
A fuse melts if the current is too large, breaking the circuit. Choose a rating above normal operating current but suitable for protecting the appliance/cable.
Circuit breakers disconnect automatically for specified faults and can be reset after the fault is corrected. A fuse must be replaced; operating speed depends on the protection device and fault.
Put switches and fuses in the live connection so opening them disconnects the appliance from live potential. Switching only neutral could leave internal parts live.
Contact between a person and live while connected to earth can drive a dangerous current through the body. Neutral is not a reason to treat any mains wiring as safe to touch.
Double-insulated appliances have insulating cases and protective insulation and do not need an earth connection to an exposed metal case. Never experiment with mains circuits; practical work uses low-voltage supplies.
Watch CP9 · Electricity and circuits · Topic 10 — Electricity and circuits
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