Circuit symbols, charge & current
By the end of this topic you'll read a circuit diagram, say exactly what current is, and link current, charge and time with one equation you have to recall.
Part 1What a circuit is
An electric current is a flow of electrical charge. For current to flow you need two things: a complete (closed) circuit with no gaps, and a source of potential difference (such as a cell or battery) to push the charge round.
Engineers draw circuits using standard circuit symbols so anyone can read them. You need to recognise and draw the common ones.
Circuit symbols to know
- Cell / battery
- The source of potential difference. A battery is two or more cells.
- Switch
- Opens (breaks) or closes (completes) the circuit.
- Resistor / variable resistor
- Limits current; the variable one can be adjusted.
- Lamp
- Transfers energy as light when current flows.
- Ammeter / voltmeter
- Ammeter measures current (in series); voltmeter measures p.d. (in parallel).
- Diode / LED · thermistor · LDR
- Diode lets current flow one way; thermistor and LDR change resistance with temperature/light.
⚠ Watch out — conventional current vs electron flow
Conventional current flows from + to − around the circuit (this is the direction you draw and use in the exam). The electrons themselves actually drift the other way (− to +), but unless a question asks specifically, always use conventional current: positive to negative.
Part 2Linking charge, current and time
Current is the rate of flow of charge — how much charge passes a point each second. Charge is measured in coulombs (C), current in amps (A), and 1 amp = 1 coulomb per second.
Equation
- Q = I t recall
- charge flow (C) = current (A) × time (s)
Worked example — charge through a lamp
A current of 0.5 A flows through a lamp for 120 s. Calculate the charge that passes through it.
⚠ Watch out — time must be in seconds
Time goes in as seconds, not minutes. A 2-minute flow is 120 s. If a question gives minutes or hours, convert first or your answer will be out by a factor of 60 (or 3600).
A charge of 90 C flows through a wire in 30 s. What is the current?
- A2700 A
- B3 A
- C0.33 A
- D60 A
Show answer
What is an electric current?
A flow of electrical charge. It needs a complete circuit and a source of potential difference to drive it.State the equation linking charge, current and time, with units.
Q = I t. Charge in coulombs (C), current in amps (A), time in seconds (s).A current of 4 A flows for 5 minutes. Calculate the charge that flows.
Time = 5 × 60 = 300 s. Q = I t = 4 × 300 = 1200 C.In which direction does conventional current flow?
From the positive (+) terminal to the negative (−) terminal around the circuit.
Resistance & potential difference
The most-used equation in the whole topic — V = I R — plus the required practical that shows resistance grows with length.
Part 1Potential difference, current and resistance
Potential difference (p.d.), measured in volts (V), is the energy transferred per unit charge as it moves between two points — it's the "push" driving the current. Resistance, measured in ohms (Ω), is how hard it is for current to flow. The bigger the resistance, the smaller the current for a given p.d.
Equation
- V = I R recall
- potential difference (V) = current (A) × resistance (Ω)
Worked example — finding resistance
A p.d. of 6 V drives a current of 0.4 A through a resistor. Calculate its resistance.
⚠ Watch out — rearrange before you panic
V = I R can find any of the three. To get current, I = V ÷ R; to get resistance, R = V ÷ I. The classic mistake is dividing the wrong way: resistance is the p.d. on top, divided by the current. Keep the units in: volts ÷ amps gives ohms.
A 12 V supply drives 3 A through a heater. What is the heater's resistance?
- A36 Ω
- B0.25 Ω
- C4 Ω
- D15 Ω
Show answer
Part 2How resistance depends on length
If you make a wire longer, its resistance goes up. In fact resistance is directly proportional to length: double the length, double the resistance. The required practical lets you test this and get a straight-line graph through the origin.
Resistance of a wire vs its length
Aim: investigate how the resistance of a wire depends on its length.
- Set up a circuit with a battery, an ammeter in series with the test wire, and a voltmeter across the test wire.
- Tape the wire to a metre ruler and connect with a flying lead so you can choose the length.
- Set the length to 10 cm. Close the switch briefly, read the current (I) and p.d. (V), then open it again.
- Calculate resistance with R = V ÷ I for that length.
- Repeat for lengths up to 100 cm (e.g. every 10 cm). Plot resistance (y) against length (x).
Control / improve: only switch on for short bursts so the wire doesn't heat up (heating raises the resistance and spoils the pattern). A straight line through the origin shows resistance ∝ length.
A 20 cm length of a wire has a resistance of 4 Ω. What is the resistance of 60 cm of the same wire?
- A4 Ω
- B1.3 Ω
- C12 Ω
- D8 Ω
Show answer
State the equation linking p.d., current and resistance.
V = I R: potential difference (V) = current (A) × resistance (Ω).A 9 V battery drives 1.5 A through a bulb. Calculate the bulb's resistance.
R = V ÷ I = 9 ÷ 1.5 = 6 Ω.In the wire required practical, why must the wire only be switched on briefly?
A continuous current heats the wire, which raises its resistance and changes the readings — so switch on only long enough to take each reading.How does the resistance of a wire change as its length increases?
It increases in direct proportion — double the length, double the resistance (a straight line through the origin).
Series & parallel circuits
The rules for current, p.d. and resistance in each type — and why adding a bulb in parallel doesn't dim the others.
Part 1Series circuits
In a series circuit there's just one loop — one path for the current. Components are connected end to end, so if one breaks, they all stop.
The current is the same everywhere in a series circuit. The total p.d. is shared between the components (it adds up to the supply p.d.). And the resistances add together: Rtotal = R1 + R2 + …, so adding a resistor always increases total resistance.
Worked example — total resistance in series
Two resistors, 4 Ω and 6 Ω, are connected in series to a 20 V supply. Find the total resistance and the current.
Part 2Parallel circuits
In a parallel circuit there's more than one branch, so the current splits. Each component gets its own loop back to the cell, so one breaking doesn't stop the others — that's why home wiring and Christmas lights use parallel.
The p.d. is the same across each branch (equal to the supply). The total current is shared between the branches and the branch currents add up to the total. Adding a resistor in parallel actually lowers the total resistance, because you've given the current another path.
⚠ Watch out — parallel resistance goes DOWN
The surprising one: adding a resistor in parallel reduces the total resistance below that of the smallest resistor, because you've opened up another route for the current. Don't add parallel resistances like you would in series — that only works for series.
Three identical lamps are connected in parallel to a 6 V battery. What is the p.d. across each lamp?
- A2 V
- B18 V
- C6 V
- D0 V
Show answer
In a series circuit, what is true about the current?
It is the same everywhere in the circuit (one path, so the same current flows through every component).How do you find the total resistance of resistors in series?
Add them up: Rtotal = R1 + R2 + … The total is always bigger than any single resistor.What is the p.d. across each branch of a parallel circuit?
The same for every branch, and equal to the supply p.d.Two 8 Ω resistors are connected in series to a 16 V supply. Find the current.
R = 8 + 8 = 16 Ω. I = V ÷ R = 16 ÷ 16 = 1 A.Why does adding a resistor in parallel decrease the total resistance?
It gives the current an extra path, so more current can flow overall for the same p.d. — which means a lower total resistance.
I–V characteristics
Reading the shape of a current–p.d. graph for a resistor, lamp and diode — plus thermistors, LDRs, and the required practical that produces them.
Part 1Three classic graphs
An I–V graph (current against potential difference) shows how a component behaves. The shape tells you whether its resistance stays constant.
An ohmic conductor (a fixed resistor at constant temperature) gives a straight line through the origin — current is directly proportional to p.d., so the resistance is constant.
A filament lamp gives an S-shaped curve. As current increases the filament gets hotter, so its resistance increases and the line bends over.
A diode only lets current flow one way. It has a very high resistance in the reverse direction, so the graph is flat (no current) until the p.d. is forward and large enough.
⚠ Watch out — the lamp's resistance rises
The filament lamp curve bends because the wire heats up, raising its resistance. A common slip is to read the flattening as the resistance falling — it's the opposite. A steeper-then-shallower curve means resistance is increasing with current.
Part 2Thermistors and LDRs
Two components change resistance with their surroundings, which makes them useful as sensors:
A thermistor's resistance falls as temperature rises. Used in thermostats and fire alarms — when it gets hot, more current flows.
An LDR (light-dependent resistor)'s resistance falls as light gets brighter. Used in automatic lights and camera exposure — in the dark its resistance is high.
Sensing components
- Thermistor
- Resistance decreases as temperature increases. Used in temperature sensors and thermostats.
- LDR
- Resistance decreases as light intensity increases. Used in light sensors and automatic street lights.
I–V characteristics of a resistor, a filament lamp and a diode
Aim: investigate how the current through a component varies with the p.d. across it.
- Connect the component in series with an ammeter and a variable resistor, with a voltmeter across the component.
- Adjust the variable resistor to change the p.d. Record several pairs of current and p.d. readings.
- Reverse the connections to the component (or swap the cell) to get negative p.d. values too.
- Plot current (y) against p.d. (x) for each component.
- Repeat for the fixed resistor, the filament lamp and the diode.
Control / improve: only switch on briefly so components (especially the lamp) don't overheat between readings. Take repeats and average to reduce random error.
A component gives a straight line through the origin on an I–V graph at constant temperature. What is it?
- AA filament lamp
- BA diode
- CAn ohmic conductor (fixed resistor)
- DA thermistor being heated
Show answer
Describe the I–V graph of an ohmic conductor.
A straight line through the origin — current is directly proportional to p.d., so the resistance stays constant.Why does the filament lamp graph curve?
As current increases the filament heats up, so its resistance increases and the line bends over (an S-shape).What does a diode do, and what does its I–V graph look like?
It only lets current flow one way. The graph shows almost no current in reverse, then a sharp rise once the forward p.d. is large enough.What happens to a thermistor's resistance as it gets hotter?
It decreases — so more current flows. (An LDR's resistance decreases as it gets brighter.)In the I–V required practical, what does the variable resistor do?
It lets you change the p.d. across (and current through) the component, so you can take a range of readings.
Mains electricity
a.c. vs d.c., the UK mains numbers you must quote, and the job of each of the three wires in a plug — plus why the earth wire saves lives.
Part 1a.c., d.c. and the UK mains
Direct current (d.c.) flows in one direction only — it's what cells and batteries supply. Alternating current (a.c.) constantly changes direction, back and forth. Mains electricity is a.c., produced by generators.
You must remember the UK mains figures: a frequency of 50 Hz (it swaps direction 50 times a second) and a potential difference of about 230 V.
⚠ Watch out — learn the mains numbers
These two values are straight recall marks: 230 V and 50 Hz. Don't mix them up (50 V / 230 Hz is wrong). And remember a.c. = mains, d.c. = battery — not the reverse.
Part 2The three-pin plug
A mains cable has three wires, each with a job and a colour you must learn:
The live wire (brown) carries the alternating p.d. from the supply — it's at about 230 V and is the dangerous one. The neutral wire (blue) completes the circuit and stays at close to 0 V. The earth wire (green & yellow) is a safety wire — it carries no current normally and only does anything if there's a fault.
If a fault connects the live wire to a metal case, the earth wire carries the current safely away to the ground, and the large current blows the fuse, breaking the circuit so you don't get a shock.
The three wires
- Live — brown
- Carries the 230 V alternating p.d. from the supply. The dangerous wire.
- Neutral — blue
- Completes the circuit; near 0 V.
- Earth — green & yellow
- Safety wire to the case; carries current only in a fault, stopping the case becoming live.
Why is the earth wire connected to the metal case of an appliance?
- ATo carry the working current during normal use
- BTo stop the case becoming live in a fault, carrying current safely away
- CTo increase the p.d. across the appliance
- DTo turn the alternating current into direct current
Show answer
State the difference between a.c. and d.c.
a.c. (alternating current) keeps changing direction; d.c. (direct current) flows one way only. Mains is a.c.; cells give d.c.Give the frequency and potential difference of the UK mains supply.
50 Hz and about 230 V.Name the three wires in a mains cable and their colours.
Live (brown), neutral (blue) and earth (green & yellow).Why can the live wire be dangerous even when an appliance is switched off?
It is still at the supply p.d. (about 230 V) relative to earth, so touching it could give a shock as your body provides a path to the ground.
Energy & power in circuits
Four equations that connect power, current, p.d., charge and energy — two to recall, two to use — and how to pick the right one.
Part 1Power in a circuit
Power is the rate of energy transfer — energy transferred per second, in watts (W). The more powerful an appliance, the faster it transfers energy from the mains. Two equations give the power of a device in a circuit.
Power equations
- P = V I recall
- power (W) = potential difference (V) × current (A)
- P = I² R recall
- power (W) = current² (A²) × resistance (Ω) — handy when you know the current and resistance
Worked example — power of a kettle
A kettle runs from the 230 V mains and draws a current of 10 A. Calculate its power.
⚠ Watch out — square the current in P = I²R
In P = I² R it's the current that's squared, not the resistance. Square I first, then multiply by R. Because of the square, doubling the current gives four times the power dissipated — which is why thick, low-resistance cables matter for high currents.
A current of 3 A flows through a 5 Ω heating element. What power is dissipated?
- A15 W
- B45 W
- C75 W
- D225 W
Show answer
Part 2Energy transferred
To find the total energy an appliance transfers, you can use either the power and time, or the charge and p.d. Both give energy in joules (J).
Energy equations
- E = P t given
- energy transferred (J) = power (W) × time (s)
- E = Q V given
- energy transferred (J) = charge flow (C) × potential difference (V)
Worked example — energy from charge and p.d.
A charge of 300 C flows through a 12 V motor. How much energy is transferred?
Worked example — energy from power and time
A 2000 W kettle is switched on for 90 s. Calculate the energy transferred.
⚠ Watch out — pick the equation that fits the data
Use E = P t when you're told the power; use E = Q V when you're told the charge. If you're given p.d. and current but not power, find power first with P = V I, then E = P t. Time always goes in as seconds.
A 60 W lamp is left on for 5 minutes. How much energy does it transfer?
- A300 J
- B18 000 J
- C12 J
- D3600 J
Show answer
Write the two power equations for a circuit.
P = V I (power = p.d. × current) and P = I² R (power = current² × resistance). Both give power in watts.A 230 V hairdryer draws 5 A. Calculate its power.
P = V I = 230 × 5 = 1150 W (1.15 kW).A 1500 W heater runs for 2 minutes. Calculate the energy transferred.
Time = 120 s. E = P t = 1500 × 120 = 180 000 J (180 kJ).240 C of charge flows through a 9 V battery. How much energy is transferred?
E = Q V = 240 × 9 = 2160 J.A 2 A current flows through a 6 Ω resistor. Calculate the power dissipated.
P = I² R = 2² × 6 = 4 × 6 = 24 W.