⚡ To find the current
Divide both sides by t.
I = Q ÷ t
current = charge ÷ time
Energy and Voltage in Circuits » Charge and Current
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 2.14, 2.15, 2.16
- What an electric current really is: the rate of flow of charge
- The equation charge = current × time, Q = I × t, which you must learn
- How to rearrange it and how to deal with mA and minutes
- Why the current in a metal is a flow of negatively charged electrons
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Unlock This CourseWhat is a current?
So far in this course you have measured currents, calculated them and seen what they do. This lesson answers a simpler question: what is actually moving?
The answer is charge. Tiny charged particles move through the wires and components of a circuit. The spec puts it in one line that you should learn word for word:
Current is the rate of flow of charge.
"Rate" means "how much each second". So the current at a point in a circuit tells you how much charge passes that point every second. A large current means a lot of charge passes each second. A small current means only a little charge passes each second.
Think of people leaving a stadium through a gate. You could count the people who pass through the gate each second. That is a rate of flow of people. An ammeter does the same job for charge: it shows how much charge passes through it each second.
Key terms:
- Charge (Q): the quantity that flows around a circuit, carried by charged particles. It is measured in coulombs (C).
- Current (I): the rate of flow of charge. It is measured in amperes (A).
The equation: charge = current × time
If the current is the charge that passes each second, then the total charge that passes is the current multiplied by the number of seconds.
charge = current × time
Q = I × t
The spec says you must know and use this relationship, so it is not given on the formulae page of the exam paper. Learn it in words and in symbols.
| Quantity | Symbol | Unit |
|---|---|---|
| Charge | Q | coulomb (C) |
| Current | I | ampere (A) |
| Time | t | second (s) |
The equation also tells you how big a coulomb is. One coulomb is the charge that passes a point when a current of 1 A flows for 1 s. So a current of 1 A means 1 C of charge passing every second, and a current of 3 A means 3 C passing every second. You can say that an ampere is a coulomb per second.
Worked example 1: finding the charge
The current in a bicycle light is 0.4 A. Calculate the charge that flows through the light in 50 s.
Equation: Q = I × t
Substitution: Q = 0.4 × 50
Answer: Q = 20 C
Rearranging the equation
You may be asked for the current or the time instead of the charge. Rearrange Q = I × t in the same way as the other equations you have met.
⏱ To find the time
Divide both sides by I.
t = Q ÷ I
time = charge ÷ current
The charge is always on top when you divide. A formula triangle works here too, with Q in the top section and I and t side by side in the bottom two sections.
Look at I = Q ÷ t. It is the sentence "current is the rate of flow of charge" written in symbols: charge divided by time is the charge that passes each second.
Worked example 2: finding the current
A charge of 360 C flows through an electric blanket in 2 minutes. Calculate the current in the blanket.
Convert: t = 2 minutes = 2 × 60 = 120 s
Equation: Q = I × t, so I = Q ÷ t
Substitution: I = 360 ÷ 120
Answer: I = 3 A
Worked example 3: finding the time
A battery charger supplies a steady current of 4 A. Calculate the time it takes for 9600 C of charge to flow. Give your answer in minutes.
Equation: Q = I × t, so t = Q ÷ I
Substitution: t = 9600 ÷ 4
Answer: t = 2400 s
In minutes: 2400 ÷ 60 = 40 minutes
Watch the units: mA and minutes
The equation only gives coulombs when the current is in amperes and the time is in seconds. Exam questions often give the current in milliamperes (mA) and the time in minutes or hours. Convert both before you put numbers into the equation.
| Conversion | What to do | Example |
|---|---|---|
| mA to A | Divide by 1000 | 150 mA = 0.15 A |
| Minutes to s | Multiply by 60 | 20 minutes = 1200 s |
| Hours to s | Multiply by 3600 | 3 hours = 10 800 s |
Worked example 4: mA and minutes together
An electric toothbrush is charged with a current of 150 mA for 20 minutes. Calculate the charge that flows.
Convert: I = 150 mA = 150 ÷ 1000 = 0.15 A and t = 20 minutes = 20 × 60 = 1200 s
Equation: Q = I × t
Substitution: Q = 0.15 × 1200
Answer: Q = 180 C
Without the conversions you would get 150 × 20 = 3000, which is far too big.
What flows in a metal wire?
The wires in a circuit are metal, usually copper. The spec asks you to know exactly what the moving charge is in a metal:
Electric current in solid metallic conductors is a flow of negatively charged electrons.
In a solid metal the atoms are fixed in place, but some of their electrons are not held to any one atom. These free electrons can move through the whole piece of metal. Each one carries a tiny negative charge. A single electron carries so little charge that it takes about six million million million electrons to make one coulomb.
With no battery connected, the free electrons wander in all directions, so there is no overall flow and no current. When you connect a battery and complete the circuit, the free electrons are pushed along the wire, all in the same overall direction. That flow of charge is the current.
🔋 Electron flow
Electrons are negative. They are repelled by the negative terminal of the battery and attracted to the positive terminal. So in the wires, electrons flow from the negative terminal round to the positive terminal.
📝 Conventional current
The arrows drawn on circuit diagrams show conventional current. It goes from the positive terminal round to the negative terminal. This rule was chosen before electrons were discovered, and it is still used today.
So the electrons in a metal wire move in the opposite direction to the conventional current. Both describe the same current. Conventional current is the direction you draw. Electron flow is what the particles actually do.
Common mistakes
- Saying that current is "the flow of charge". The full answer is the rate of flow of charge.
- Mixing up charge and current. Charge (in coulombs) is the amount that has passed. Current (in amperes) is how much passes each second.
- Putting minutes or mA straight into Q = I × t. Convert to seconds and amperes first.
- Dividing the wrong way up. Charge is always on top: I = Q ÷ t and t = Q ÷ I.
- Mixing up the symbols. Q is charge and its unit is C. I is current and its unit is A. The letter C is a unit, never the symbol for current.
- Saying that electrons flow from positive to negative. Electrons are negative, so they flow from the negative terminal to the positive terminal.
- Saying that positive charges move in a metal wire. In a solid metal only the electrons flow.
Exam-style question
A toy boat has a small electric motor connected to a battery by copper wires. The current in the motor is 0.25 A.
(a) State what is meant by the term electric current. [1 mark]
(b) The motor runs for 3 minutes. Calculate the charge that flows through the motor. Give the unit. [4 marks]
(c) Describe the particles that flow in the copper wires and the direction in which they move around the circuit. [2 marks]
(d) The battery is replaced. A charge of 96 C now flows through the motor in 2 minutes. Calculate the new current in the motor. Give your answer in mA. [3 marks]
Model answer
(a) Current is the rate of flow of charge (1).
(b) t = 3 minutes = 180 s (1). Q = I × t = 0.25 × 180 (1) = 45 (1) C (1).
(c) Negatively charged electrons (1). They flow from the negative terminal of the battery to the positive terminal (1).
(d) t = 2 minutes = 120 s (1). I = Q ÷ t = 96 ÷ 120 = 0.8 A (1) = 800 mA (1).
Exam tip
Parts (b) and (d) both give the time in minutes, and part (d) also wants the answer in mA. Change minutes into seconds as your first line of working, do the calculation in amperes, and only multiply by 1000 to get mA at the very end.