How is electric current defined?

rate of flow of charge. I = ΔQ ÷ Δt.

In I = nAvq, what is n?

the number of charge carriers per unit volume. It is a property of the material.

The same current flows in a thick wire and a thin wire of the same metal. In which do the electrons drift faster?

the thin wire. A smaller area needs a higher speed to carry the same current.

Which of these charges is impossible for any object to have?

2.4 × 10⁻¹⁹ C. Charge comes in whole multiples of 1.6 × 10⁻¹⁹ C, and this is one and a half.

Current and charge carriers · Cambridge A Level Physics

In plain words

A current is charge on the move. In a metal wire the carriers are electrons, and although a lamp lights the instant you flick the switch, the electrons themselves drift along slower than a snail. There are just an enormous number of them.

4 things to know

Electric current is the rate of flow of charge: I = ΔQ ÷ Δt, so Q = It. One ampere is one coulomb per second.
Charge is quantised: it comes only in whole multiples of e = 1.60 × 10⁻¹⁹ C.
For a conductor, I = nAvq. Here n is the number of charge carriers per unit volume, A is the cross-sectional area, v is the carriers' average (drift) speed and q is the charge on each one.
Metals have an enormous n, so they conduct well. Insulators have almost no free carriers, and semiconductors are in between. That is why materials differ so hugely in how well they conduct.

Worked example

A copper wire of cross-sectional area 1.0 × 10⁻⁶ m² carries 2.0 A. Copper has 8.5 × 10²⁸ free electrons per m³. Find their average speed.

I = nAvq, so v = I ÷ (nAq).
= 2.0 ÷ (8.5 × 10²⁸ × 1.0 × 10⁻⁶ × 1.60 × 10⁻¹⁹).
= 1.5 × 10⁻⁴ m/s: a fraction of a millimetre each second.

Tips and tricks

Conventional current flows from positive to negative. Electrons go the other way.
A thinner wire carrying the same current has a higher drift speed, because A is smaller.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Current and charge carriers: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

How is electric current defined?
- energy per unit charge
- rate of flow of charge (the answer)
- charge per unit volume
- force per unit charge
I = ΔQ ÷ Δt.
In I = nAvq, what is n?
- the number of electrons in the wire
- the number of charge carriers per unit volume (the answer)
- the number of turns on a coil
- the number of amperes
It is a property of the material.
The same current flows in a thick wire and a thin wire of the same metal. In which do the electrons drift faster?
- the thick wire
- the thin wire (the answer)
- neither: they are the same
- it depends on the length
A smaller area needs a higher speed to carry the same current.
How much charge passes when a current of 2.0 A flows for 30 s?
- 0.067 C
- 15 C
- 32 C
- 60 C (the answer)
Q = It.
Which of these charges is impossible for any object to have?
- 1.6 × 10⁻¹⁹ C
- 2.4 × 10⁻¹⁹ C (the answer)
- 3.2 × 10⁻¹⁹ C
- 4.8 × 10⁻¹⁹ C
Charge comes in whole multiples of 1.6 × 10⁻¹⁹ C, and this is one and a half.

5 questions

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Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Current and charge carriers

Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org

Name ______________________________ Date ______________

A current of 0.50 A flows for 2.0 minutes. Find the charge that passes, and the number of electrons.[2]
Show answerHide answer
60 C, and 3.8 × 10²⁰ electrons. 60 ÷ 1.60 × 10⁻¹⁹.
I got this one
A wire of cross-sectional area 2.0 × 10⁻⁶ m² carries 4.0 A. It has 1.0 × 10²⁹ free electrons per m³. Find their average speed.[3]
Show answerHide answer
1.3 × 10⁻⁴ m/s. 4.0 ÷ (1.0 × 10²⁹ × 2.0 × 10⁻⁶ × 1.60 × 10⁻¹⁹).
I got this one
Explain why a lamp lights almost at once, even though the electrons in the wires drift very slowly.[2]
Show answerHide answer
There are free electrons all the way round the circuit, and they all start to move at almost the same moment when the switch is closed. No electron has to travel from the switch to the lamp.
I got this one

Answers: Current and charge carriers

1. 60 C, and 3.8 × 10²⁰ electrons. 60 ÷ 1.60 × 10⁻¹⁹.
2. 1.3 × 10⁻⁴ m/s. 4.0 ÷ (1.0 × 10²⁹ × 2.0 × 10⁻⁶ × 1.60 × 10⁻¹⁹).
3. There are free electrons all the way round the circuit, and they all start to move at almost the same moment when the switch is closed. No electron has to travel from the switch to the lamp.