D. Physics: Principles and Applications of Electricity · Electricity: Charges, Circuits and Energy

Current Electricity: Electric Current and Potential Difference

D2.1 D2.3 A1.4About 75 minutes

Learning goals

I can explain what is needed for current electricity to flow.
I can define electric current and calculate it with I = Q ÷ t, using amperes, coulombs and seconds.
I can define potential difference and calculate it with V = E ÷ Q, using volts, joules and coulombs.
I can tell the difference between electron flow and conventional current, and between DC and AC.
I can compare static electricity and current electricity.

Words to know

electric current (I)
The amount of charge passing a point in a circuit each second. I = Q ÷ t. Unit: the ampere (A).

ampere (A)
The SI unit of current. 1 A = 1 coulomb per second (1 C/s). Small currents are measured in milliamperes: 1000 mA = 1 A.

potential difference (V)
The difference in electric potential energy per unit of charge between two points in a circuit. V = E ÷ Q. Also called voltage. Unit: the volt (V).

volt (V)
The SI unit of potential difference. 1 V = 1 joule per coulomb (1 J/C).

electric potential energy
Energy stored because of the positions of electric charges, like the energy of a skier at the top of a hill.

electron flow
The actual movement of electrons in a circuit: from the negative terminal, through the circuit, to the positive terminal.

conventional current
The direction chosen by scientists long before electrons were discovered: from the positive terminal, through the circuit, to the negative terminal.

direct current (DC)
Current that flows in one direction only, as from a battery.

alternating current (AC)
Current that reverses direction many times each second, as from a wall outlet. In Canada it reverses with a frequency of 60 Hz.

From sparks to steady flow

A doorknob spark is over in a fraction of a second. A flashlight, though, can stay on for hours. The difference is that a flashlight has a source of energy (the batteries) that keeps pushing charge around a complete loop of conductors.

For current electricity you need:

A source of electrical energy that creates a potential difference, such as a cell, battery, solar cell or generator.
A closed path of conductors (a circuit) from one terminal of the source, through the devices, and back to the other terminal.

Electric current: how much charge flows each second

Electric current (symbol I) is the amount of charge (Q) that passes a point in the circuit in a certain time (t):

I = Q ÷ t

Q is in coulombs (C), t in seconds (s), and I in amperes (A), often shortened to amps.
1 A means 1 coulomb of charge passes a point every second. That is about 6.24 × 10¹⁸ electrons per second!
Current is measured with an ammeter.

Inside the wire, the electrons drift slowly, often less than a millimetre per second. But the wire is full of electrons from end to end, so when the switch closes, they all start moving at almost the same moment and the bulb lights instantly. It is like pushing marbles into a full tube: one goes in, and one pops out the far end right away.

Worked example

Example 1: Find the current

30 C of charge passes through a toaster's heating element in 10 s. What is the current?

Write what you know: Q = 30 C, t = 10 s. Find I.
I = Q ÷ t
I = 30 C ÷ 10 s

I = 3.0 A

Worked example

Example 2: Find the charge

A phone draws a current of 0.50 A for 2.0 minutes. How much charge flows?

Change minutes to seconds: 2.0 min × 60 s/min = 120 s.
Rearrange I = Q ÷ t to get Q = I × t.
Q = 0.50 A × 120 s

Q = 60 C. Always convert time to seconds first.

Potential difference: how much energy each coulomb carries

A battery uses chemical reactions to give energy to the charges. Potential difference (symbol V, also called voltage) tells you how much energy (E) each coulomb of charge (Q) gains in the source, or loses in a device:

V = E ÷ Q

E is in joules (J), Q in coulombs (C), and V in volts (V).
A 1.5 V AA cell gives 1.5 J of energy to every coulomb of charge that passes through it.
Potential difference is always measured between two points, with a voltmeter.

The charges are not used up in a circuit. They carry energy from the source to the devices (loads), give it up there (as light, heat, motion or sound), and return to the source to pick up more.

The ski hill model of a circuit. The chairlift (battery) lifts skiers (charges), giving them energy. They give up that energy on the ski run (the load) and return to the lift. The height of the hill is like the potential difference; the number of skiers passing per second is like the current. Skiers are never used up.

Worked example

Example 3: Find the potential difference

A battery gives 18 J of energy to 2.0 C of charge. What is the potential difference of the battery?

E = 18 J, Q = 2.0 C. Find V.
V = E ÷ Q = 18 J ÷ 2.0 C

V = 9.0 V. Each coulomb gains 9 J: it is a 9 V battery.

Worked example

Example 4: Find the energy

A 12 V car battery moves 50 C of charge through the starter motor. How much energy does the battery supply?

Rearrange V = E ÷ Q to get E = V × Q.
E = 12 V × 50 C = 12 J/C × 50 C

E = 600 J

Which way does current flow?

In the 1700s, scientists decided that current flows from the positive (+) terminal to the negative (−) terminal. This is called conventional current. Much later, they discovered that in metal wires the moving particles are electrons, which move the other way: from − to +. This is called electron flow.

Both descriptions predict the same results in a circuit. Most circuit diagrams and later physics courses use conventional current, so in this unit, an arrow labelled "current" means conventional current unless we say electron flow.

In the same circuit, conventional current (solid arrow) is shown leaving the + terminal, while electrons (dashed arrow) actually leave the − terminal and move the opposite way around the loop.

Direct current and alternating current

Direct current (DC): charges flow in one direction. Batteries, solar cells and phone chargers' outputs are DC.
Alternating current (AC): charges move back and forth, reversing direction many times a second. Wall outlets in Canada supply AC at about 120 V and 60 Hz (60 complete back-and-forth cycles per second). Large appliances such as stoves and dryers use 240 V.

This unit's circuits are DC circuits, the kind named in the curriculum.

Current over time. DC (left) stays steady in one direction. AC (right) rises, falls, and reverses direction over and over.

	Static electricity	Current electricity
Charges	Build up and stay on a surface	Flow continuously
Path	No closed path needed	Needs a closed circuit
Usual materials	Insulators hold the charge	Conductors carry the charge
Energy release	All at once, in a discharge (spark)	Steadily, as long as the source works
Examples	Balloon on a wall, doorknob spark, lightning	Flashlight, phone, fridge, streetlights

Static and current electricity compared.

Formula triangles and units

I = Q ÷ t, so Q = I × t and t = Q ÷ I.
V = E ÷ Q, so E = V × Q and Q = E ÷ V.
Convert to base units first: minutes → seconds (× 60), hours → seconds (× 3600), mA → A (÷ 1000), kJ → J (× 1000).
Write the unit with every number. If the units do not work out, the formula is upside down.

Hands-on activity

Label detective: chargers and batteries

You need: 3 or 4 chargers, power adapters or batteries from around your home (do not plug anything in or open anything), a notebook, a calculator.

Find the printed label on each item. Look for Input and Output, a voltage in V, and a current in A or mA.
The symbol ⎓ (a solid line over a dashed line) means DC. The symbol ~ means AC. Record which each one uses.
For a charger with output such as "5 V ⎓ 2 A", calculate: how much charge flows in 1 hour? (Q = I × t = 2 A × 3600 s = 7200 C.) How much energy does that charge carry? (E = V × Q = 5 V × 7200 C = 36 000 J.)
Many batteries list capacity in mAh (milliampere-hours). Convert one to coulombs: 1 mAh = 0.001 A × 3600 s = 3.6 C. So a 3000 mAh battery holds a charge flow of 3000 × 3.6 = 10 800 C.

What to look for: inputs are usually AC (from the wall, often "100–240 V ~"), and outputs to your device are DC at a low voltage.

Coding extension (A1.4): write a short program that asks for a current and a time in minutes and prints the charge. In Python:

I = float(input("Current in A: ")) minutes = float(input("Time in min: ")) print("Charge =", I * minutes * 60, "C")

With 0.5 and 2, it prints Charge = 60.0 C (Example 2).

Safety (grown-up note): Only read labels. Never open batteries or chargers, and never put anything into a wall outlet.

Just for fun

Electrons in a wire are surprisingly slow walkers: they often drift less than a millimetre each second. If one electron had to travel all the way from the battery around a long circuit, the trip could take hours. Luckily, the bulb does not wait for it: every electron in the wire starts moving at once, like a line of people all stepping forward together.

Your turn

What two things does a circuit need for current to flow?

A current of 2.0 A flows for 15 s. How much charge passes?

240 C of charge passes through a lamp in 2.0 minutes. What is the current?

A battery gives 27 J of energy to 3.0 C of charge. What is its potential difference?

How much energy does a 1.5 V cell give to 40 C of charge?

Which way do electrons move around a circuit? Which way is conventional current?

Is the electricity from a wall outlet in Canada AC or DC? From a battery?

More practice: warm-up

What is the SI unit of current?

What is the SI unit of potential difference?

Convert 350 mA to amperes.

What does a voltage of 1.5 V mean in joules and coulombs?

True or false: charges are used up as they pass through a light bulb.

More practice: on your own

A flashlight bulb carries 0.40 A. How long does it take for 96 C of charge to pass through it?

A 9.0 V battery supplies 4.5 kJ of energy. How much charge did it move?

A current of 250 mA flows for 1.0 hour. Find the charge in coulombs.

Using the ski hill model, what would a higher-voltage battery be like? What would a bigger current be like?

Give two differences between static electricity and current electricity.

Challenge

A phone battery is rated 3.85 V and 4000 mAh. How much charge and how much energy can it deliver when fully charged?

A lightning flash transfers about 15 C of charge in 0.0010 s. What is the average current? Compare it with a 5 A toaster.

Write a Python program that asks for a potential difference (V) and a charge (C) and prints the energy in joules. Show the output for 12 V and 50 C.

Check your understanding

Quiz

Electric current is:

60 C passes through a device in 30 s. What is the current?

1 volt is equal to:

A 6.0 V battery moves 10 C of charge. How much energy does it supply?

In a metal wire, electrons move:

What kind of current does a battery supply?

For parents and teachers

Big idea: This lesson defines the two key quantities of current electricity (D2.1, D2.3): current (charge per second, I = Q ÷ t, in amperes) and potential difference (energy per charge, V = E ÷ Q, in volts). The optional Python lines practise A1.4 (coding to model science relationships).

Common difficulties:

Mixing up current and voltage. Current is how much charge flows per second; voltage is how much energy each coulomb carries. The ski hill model helps.
Forgetting to convert minutes or hours to seconds, and mA to A.
Thinking batteries 'run out of electrons'. A battery runs out of chemical energy; the electrons were already in the wires.

How to help: Read charger labels together and do one calculation from a real label. Only read the labels: never open batteries or put anything in an outlet.