F. Electricity and Magnetism · Electricity and MagnetismCharge, Current and Potential Difference: Conventional Current and Electron Flow
F2.1 F3.3 A1.12 A1.13About 70 minutes
Learning goals- I can define electric charge, current, potential difference, power and energy, with their symbols and SI units.
- I can use Q = IΔt, Q = Ne, V = E ÷ Q and P = VI to solve problems.
- I can explain the difference between conventional current and electron flow and draw both on a circuit diagram.
- I can report answers with correct units and significant digits.
Words to know
electric charge (Q)
A property of protons (+) and electrons (−). Measured in coulombs (C).
elementary charge (e)
The size of the charge on one proton or one electron: e = 1.60 × 10⁻¹⁹ C.
electric current (I)
The rate at which charge passes a point: I = Q ÷ Δt. Measured in amperes (A); 1 A = 1 C/s.
potential difference (V)
The electrical energy gained or lost by each coulomb of charge between two points: V = E ÷ Q. Measured in volts (V); 1 V = 1 J/C. Also called voltage.
conventional current
The direction positive charge would move: out of the positive terminal, through the circuit, back to the negative terminal.
electron flow
The direction electrons actually move in a metal wire: out of the negative terminal, through the circuit, back to the positive terminal.
direct current (DC)
Current that flows in one direction only, like the current from a battery.
electric power (P)
The rate at which electrical energy is transformed: P = E ÷ Δt = VI. Measured in watts (W); 1 W = 1 J/s.
Flip the switch
When you flip a light switch, the light comes on at once. You might picture electrons racing from the switch to the bulb. In fact, electrons in a copper wire drift very slowly, often less than a millimetre per second. The wire is already full of free electrons. When the circuit closes, they all start moving together, like a long line of people on a crowded escalator who all start moving at the same moment.
This unit is about electricity and magnetism: how charges move in circuits, how moving charges make magnetic fields, and how magnetic fields make electricity in generators and transformers. That is how almost every kilowatt-hour in Ontario is produced and delivered. First, we need precise language.
Remember from Grade 9
In Grade 9 (SNC1W) you learned that atoms contain protons and electrons, that current is measured in amperes with an ammeter connected in series, that potential difference is measured in volts with a voltmeter connected in parallel, and that resistance is measured in ohms. You used Ohm's law, V = IR, built series and parallel circuits, and calculated power and energy in kilowatt-hours. You also met the idea of conventional current. Grade 11 makes all of this quantitative and links it to magnetism.
Charge and the coulomb
Charge comes in tiny packages. Every electron carries a charge of −e and every proton carries +e, where
e = 1.60 × 10⁻¹⁹ C (the elementary charge).
A coulomb is a lot of electrons. If N electrons pass a point, the total charge is
Q = Ne
So 1 C is the charge of 1 ÷ (1.60 × 10⁻¹⁹) = 6.25 × 10¹⁸ electrons.
Current: charge per second
Electric current is how much charge passes a point each second:
I = Q ÷ Δt, which rearranges to Q = IΔt
I is in amperes (A), Q in coulombs (C) and Δt in seconds (s). A current of 1 A means 1 C, or 6.25 × 10¹⁸ electrons, passes every second. Small currents are often given in milliamperes: 1 mA = 0.001 A.
Potential difference: energy per charge
A battery does not "make" electrons. The wire already has them. The battery gives energy to each coulomb of charge that passes through it. The charges then give that energy up in the loads (lamps, heaters, motors).
Potential difference is the energy change for each coulomb:
V = E ÷ Q, which rearranges to E = QV
One volt is one joule per coulomb. A 9.0 V battery gives every coulomb that passes through it 9.0 J of energy. A 120 V wall outlet in a Canadian home gives every coulomb about 120 J, which is why wall outlets are far more dangerous than batteries.
Power: energy per second
Combine the two ideas. Each second, I coulombs pass, and each coulomb carries V joules. So the energy transformed each second is
P = VI and E = PΔt = VIΔt
P is in watts (W). Electricity bills use the kilowatt-hour: 1 kW·h = 1000 W × 3600 s = 3.6 × 10⁶ J.
Conventional current and electron flow
In the 1700s, Benjamin Franklin named the two kinds of charge "positive" and "negative". Scientists then described current as positive charge flowing from + to −. More than a century later, scientists learned that in metal wires the charges that actually move are electrons, which are negative and move from − to +.
By then, the rules and diagrams were all written for positive flow. So physicists kept it, and gave the two directions names:
- Conventional current: from the positive terminal, through the external circuit, to the negative terminal. Electrical engineers and most textbooks use this.
- Electron flow: from the negative terminal, through the external circuit, to the positive terminal. This is what electrons really do in a wire.
For calculating current, potential difference and resistance, the choice makes no difference: positive charge moving one way has the same effect as negative charge moving the other way. It does matter for the hand rules you will learn later in this unit: right-hand rules use conventional current, left-hand rules use electron flow. In this unit, an arrow labelled I means conventional current unless it says "electron flow".
| Quantity | Symbol | SI unit | Key equation | Meter |
|---|
| charge | Q | coulomb (C) | Q = Ne = IΔt | — |
| current | I | ampere (A) = C/s | I = Q ÷ Δt | ammeter, in series |
| potential difference | V | volt (V) = J/C | V = E ÷ Q | voltmeter, in parallel |
| resistance | R | ohm (Ω) = V/A | R = V ÷ I | ohmmeter (circuit off) |
| power | P | watt (W) = J/s | P = VI = E ÷ Δt | — |
| energy | E | joule (J); kW·h | E = QV = PΔt | electricity meter (kW·h) |
Worked exampleExample 1: Counting electrons
A flashlight bulb carries a current of 0.50 A for 2.0 min. (a) How much charge passes through it? (b) How many electrons is that?
- Convert time to seconds: Δt = 2.0 min × 60 s/min = 120 s.
- (a) Q = IΔt = (0.50 A)(120 s) = 60 C.
- (b) Q = Ne, so N = Q ÷ e = 60 C ÷ (1.60 × 10⁻¹⁹ C) = 3.75 × 10²⁰.
- Both given values have two significant digits, so round to two: 3.8 × 10²⁰ electrons.
60 C, which is about 3.8 × 10²⁰ electrons.
Worked exampleExample 2: Energy, charge and time
A 9.0 V battery transfers 36 J of energy to the charges passing through it. The current is 0.20 A. (a) How much charge passed through? (b) For how long was the circuit on?
- (a) V = E ÷ Q, so Q = E ÷ V = 36 J ÷ 9.0 V = 4.0 C.
- (b) Q = IΔt, so Δt = Q ÷ I = 4.0 C ÷ 0.20 A = 20 s.
- Check with power: P = VI = (9.0)(0.20) = 1.8 W, and E = PΔt = (1.8 W)(20 s) = 36 J. ✓
4.0 C of charge, for 20 s.
Worked exampleExample 3: Charging a phone
A phone charger supplies 2.0 A at 5.0 V for 1.5 h. Find the power and the energy delivered, in joules and in kilowatt-hours.
- P = VI = (5.0 V)(2.0 A) = 10 W.
- Δt = 1.5 h × 3600 s/h = 5400 s, so E = PΔt = (10 W)(5400 s) = 54 000 J = 5.4 × 10⁴ J.
- In kilowatt-hours: E = (0.010 kW)(1.5 h) = 0.015 kW·h. (Check: 0.015 × 3.6 × 10⁶ J = 5.4 × 10⁴ J ✓)
10 W; 5.4 × 10⁴ J, or 0.015 kW·h.
Hands-on activityLabel detective
You need: 3 or 4 electrical items with a label (a phone charger, a lamp, a kettle or toaster, a pack of AA batteries), paper and a calculator. Grown-up note: read labels only on items that are unplugged, and never open a device or a charger.
- Look for the rating plate or printed label. Write down any values with units V, A, mA, W or mAh. Chargers usually show an input (about 120 V AC for Canadian outlets) and an output (often 5 V DC for phones).
- For each item, use P = VI to find the missing value (power if V and I are given, current if V and P are given).
- For a battery or power bank marked in mAh, convert to coulombs: 1 mAh = 0.001 A × 3600 s = 3.6 C.
- Decide: which items use AC and which use DC?
What to look for: a 1500 W kettle on 120 V draws I = 1500 ÷ 120 = 12.5 A. A charger with output 5 V, 2 A delivers 10 W. A 2500 mAh battery stores 2500 × 3.6 = 9000 C of charge. Wall-plugged appliances run on AC; batteries and the output side of phone chargers are DC.
Your turn
1A current of 3.0 A flows for 5.0 s. How much charge passes?
Q = IΔt = (3.0 A)(5.0 s) = 15 C.
22.4 C of charge passes a point in 0.80 s. What is the current?
I = Q ÷ Δt = 2.4 ÷ 0.80 = 3.0 A.
3How many electrons make up 1.0 C of charge?
N = Q ÷ e = 1.0 ÷ (1.60 × 10⁻¹⁹) = 6.25 × 10¹⁸ electrons (6.3 × 10¹⁸ to two significant digits).
4A 1.5 V cell does 6.0 J of work on the charge passing through it. How much charge passed?
Q = E ÷ V = 6.0 ÷ 1.5 = 4.0 C.
5In the external circuit (outside the battery), which way does conventional current go? Which way do electrons go?
Conventional current goes from the positive (+) terminal to the negative (−) terminal. Electrons go the opposite way, from − to +.
6A 12 V car battery delivers 50 A to the starter motor for 2.0 s. Find the charge and the energy delivered.
Q = IΔt = (50)(2.0) = 100 C. E = QV = (100 C)(12 V) = 1200 J (1.2 × 10³ J).
7A toaster draws 7.5 A from a 120 V outlet. What is its power?
P = VI = (120)(7.5) = 900 W.
Just for funBenjamin Franklin had a 50–50 chance of calling the right kind of charge "positive". He picked the one that made electrons negative, and physicists have been drawing current arrows "backwards" ever since.
More practice: warm-up
1What is the SI unit of current, and what is it equal to in coulombs and seconds?
The ampere (A). 1 A = 1 C/s.
2What is 1 volt equal to in joules and coulombs?
3What is the value of the elementary charge e?
4In a cell symbol, is the long thin plate the positive or the negative terminal?
The long plate is positive; the short thick plate is negative.
5Convert 250 mA to amperes.
More practice: on your own
1A lamp draws 0.25 A for 1.0 h. How many electrons pass through it?
Q = IΔt = (0.25)(3600) = 900 C. N = Q ÷ e = 900 ÷ (1.60 × 10⁻¹⁹) = 5.6 × 10²¹ electrons.
24.0 × 10¹⁹ electrons pass a point in 2.0 s. Find the current.
Q = Ne = (4.0 × 10¹⁹)(1.60 × 10⁻¹⁹) = 6.4 C. I = Q ÷ Δt = 6.4 ÷ 2.0 = 3.2 A.
3A 6.0 V battery gives 540 J to the charges passing through it in 1.5 min. Find the current.
Q = E ÷ V = 540 ÷ 6.0 = 90 C. Δt = 1.5 × 60 = 90 s. I = Q ÷ Δt = 90 ÷ 90 = 1.0 A.
4A 1500 W kettle runs on 120 V for 3.0 min. Find the current and the energy used.
I = P ÷ V = 1500 ÷ 120 = 12.5 A (about 13 A). E = PΔt = (1500)(180) = 2.7 × 10⁵ J (0.075 kW·h).
5Why do physicists still use conventional current if electrons move the other way?
The convention was set before electrons were discovered, and all the laws and diagrams were written for it. For current, voltage and resistance calculations, positive charge moving one way is equivalent to negative charge moving the opposite way, so the results are the same. You only need to be careful to match the hand rule (right or left) to the direction you use.
Challenge
1Suppose a lightning stroke carries an average current of 30 kA for 50 μs. How much charge is transferred, and how many electrons is that?
Q = IΔt = (3.0 × 10⁴ A)(5.0 × 10⁻⁵ s) = 1.5 C. N = 1.5 ÷ (1.60 × 10⁻¹⁹) ≈ 9.4 × 10¹⁸ electrons.
2A phone battery is rated 3000 mAh at 3.85 V. How much charge and how much energy can it store when full?
Charge: 3000 mAh = 3.000 A × 3600 s = 1.08 × 10⁴ C. Energy: E = QV = (1.08 × 10⁴ C)(3.85 V) ≈ 4.16 × 10⁴ J (about 11.6 W·h).
3A copper wire carries 2.0 A. (a) How many electrons pass a point each second? (b) The electrons drift slower than 1 mm/s. Explain why a lamp at the end of a long wire still lights almost instantly.
(a) N per second = I ÷ e = 2.0 ÷ (1.60 × 10⁻¹⁹) = 1.25 × 10¹⁹ electrons per second. (b) The wire is already full of free electrons. When the switch closes, the electric push from the battery is set up through the whole circuit almost instantly, so electrons everywhere in the wire, including those in the lamp, start drifting at the same time. The lamp does not wait for electrons from the switch to reach it.
Quiz
1. What is electric current?
2. A current of 2.0 A flows for 30 s. How much charge passes?
3. A 3.0 V battery moves 5.0 C of charge. How much energy does it give the charge?
4. Which statement about conventional current is correct?
5. Which unit is equivalent to a volt?
6. A 60 W lamp runs on 120 V. What current does it draw?
Big idea: This lesson sets up the vocabulary for the whole unit (F2.1) and the difference between conventional current and electron flow (F3.3), which matters later for the hand rules. Most of the ideas were met in Grade 9; what is new is the quantitative link between charge, current, energy and potential difference.
How to help: Ask your teen to explain each quantity in their own words: "current is coulombs per second", "voltage is joules per coulomb". The label activity is a good kitchen-table conversation; keep all devices unplugged while reading labels.
Common difficulties:
- Forgetting to convert minutes or hours to seconds before using Q = IΔt or E = PΔt.
- Mixing up which terminal is which on a cell symbol (the long plate is positive).
- Thinking the battery "supplies the electrons". It supplies energy; the electrons are already in the wire.
- Calculator entry of scientific notation: use the EE or ×10ˣ key for 1.60 × 10⁻¹⁹, not "× 10 ^" typed separately, which can cause errors.
- Rounding too early. Keep extra digits until the final answer, then round to the least number of significant digits in the data.