Electricity

9.1 Electric current

Electric current is a flow of charge carriers. In a metal the carriers are free electrons, and in a salt solution they are positive and negative ions.

$Q = It$

Current is the rate of flow of charge, so 1 coulomb is the charge that passes when 1 A flows for 1 s.

Charge is quantised: it comes in whole-number multiples of the elementary charge $e = 1.60 \times 10^{-19}$ C. You can never have half an electron's charge on a free particle.

The transport equation

For a conductor of cross-section $A$, with $n$ charge carriers per unit volume, each carrying charge $q$ and moving with mean drift speed $v$:

$I = Anvq$

In a volume $Avt$ there are $Avtn$ carriers, with total charge $Avtnq$. Dividing by the time $t$ gives the current.

A thinner section of the same wire has the same current but a smaller area, so the electrons drift faster.

9.2 Potential difference and power

The potential difference across a component is the energy transferred per unit charge passing through it:

$V = \frac{W}{Q}$

So 1 V is 1 J/C.

Electrical power

Power is the rate of energy transfer. Since $W = VQ$ and $Q = It$:

$P = VI = I^2R = \frac{V^2}{R}$

Use whichever form has the quantities you know. Energy transferred is $W = VIt$.

9.3 Resistance and resistivity

Resistance is the ratio of the potential difference across a component to the current through it:

$R = \frac{V}{I}$

The unit is the ohm, where $1\ \Omega = 1$ V/A.

I–V characteristics

• Metallic conductor at constant temperature: a straight line through the origin, so the resistance is constant.
• Filament lamp: an S-shaped curve. As the current increases, the filament gets hotter. Its ions vibrate more, the electrons collide with them more often, and the resistance increases.
• Semiconductor diode: almost no current in reverse. In the forward direction, the current rises sharply above about 0.6 V, so the resistance falls.

Resistance at a point on a curve is $V/I$ at that point, not the gradient of the tangent.

Ohm's law

Resistivity

$R = \frac{\rho L}{A}$

where $\rho$ is the resistivity of the material (Ω m), $L$ is the length and $A$ is the cross-sectional area. Resistivity is a property of the material, and resistance is a property of a particular sample.

LDRs and thermistors

• Light-dependent resistor (LDR): resistance decreases as light intensity increases.
• Thermistor (negative temperature coefficient): resistance decreases as temperature increases.

In both, more energy frees more charge carriers, and that outweighs other effects. Chapter 10 shows how these are used in sensors.