1. The current in a wire is like water flowing down a pipe. The amount of water that flows depends on the flow rate and the time. It’s the same with electricity — current is the rate of flow of charge.

   I = △Q/△t - Where I is the current in amperes, △Q is the charge in coulombs, and △t is the time taken in seconds.

   Remember that conventional current flows from + to -, the opposite way from electron flow.

2. The coulomb is the unit of charge.

   One coulomb (C) is defined as the amount of charge that passes in 1 second when the current is 1 ampere.

3. You can measure the current flowing through part of a circuit using an ammeter. This is the circuit symbol for an ammeter - Attach an ammeter in series with the component you’re investigating.

Potential Difference is the Work Done per Unit Charge

1. To make electric charge flow through a conductor, you need to do work on it.

2. Potential difference, or voltage, is defined as the work done per unit charge moved: V = W/Q - W is the work done in joules. It’s the energy transferred in moving the charge.

   The potential difference across a component is 1 volt (V) when you do 1 joule of work moving 1 coulomb of charge through the component. This defines the volt. 1V = 1 J C ¯¹.

   Back to the ‘water analogy’ again. The p.d. is like the pressure that’s forcing the water along the pipe.

   E.g. 6J of work moving each coulomb of charge through the resistor, so the p.d. across it is 6V. The energy gets converted to heat.

3. You can measure the potential difference across a component using a voltmeter. This is the circuit symbol for a voltmeter - the maximum value that a voltmeter or ammeter can measure is called the full scale deflection.

4. Remember, the potential difference across components in parallel is the same, so the voltmeter should be connected in parallel with the component you’re investigating.

Charge Carriers in Liquids and Gases are Ions

1. A current is the rate of flow of charged particles (called charge carries). In a circuit, the charge carriers are free electrons (sometimes called conduction electrons), but there are other types of charge carrier.

2. A flow of positively-charged particles produces exactly the same current as an equal flow of negatively-charged particles in the opposite direction. This is why we use conventional current, defined as ‘in the same direction as a flow of positive charges’.

3. Ionic crystal like sodium chloride are insulators. Once molten, though, the liquid conducts. Positive and negative ions are the charge carriers. The same thing happens in an ionic solution like copper sulfate solution.

4. Gases are insulators, but if you apply a high enough voltage electrons get ripped out of atoms, giving you ions along a path. You get a spark.

Uses of ions in air include creating a dramatic backdrop to a Gothic horror story, and bringing the creations of mad scientists to life.

The Mean Drift Velocity is the Average Velocity of the Charge Carriers

When current flows through a wire, you might imagine the electrons all moving uniformly in the same direction. In fact, they move randomly in all directions, but tend to drift one way. The mean drift velocity is just the average velocity and it’s much, much less than the electrons’ actual speed. (Their actual speed is about 10⁶ ms¯¹.)

The Current Depends on the Mean Drift Velocity:

The current is given by the equation:

I = nqvA

where:

• I = electrical current (A)

• n= number density of charge carriers (m¯³), (number per unit volume)

• q = charge on each charge carrier (C)

• v = mean drift velocity (ms¯¹)

• A = cross-sectional area (m²)

  • The charge on an electron, e, is -1.60 × 10^-19

Different Materials have Different Numbers of Charge Carriers

1. In a metal, the charge carriers are free electrons — they’re the ones from the outer shell of each atom. Thinking about the formula I = nqvA, there are loads of charge carriers per unit volume, making n big. The drift velocity is small, even for a high current.

2. Semiconductors have fewer charge carriers, so the drift velocity needs to be higher to give the same current.

A perfect insulator wouldn’t have any charge carriers, so n = 0 in the formula and you’d get no current. Real insulators have a very small n.

Practice Questions

Q1 Describe in words and symbols how current and charge are related.

Q2 Define potential difference.

Q3 What happens to the current in a wire if the mean drift velocity of the electrons is halved?

Q4 Describe how metals, semiconductors and insulators differ in terms of n.