What resistance is

1. Resistance is the opposition a component offers to the flow of charge through it, so a large resistance means it is hard to drive a current through that component.
2. In a metal the delocalised electrons are free to drift when a potential difference is applied, but the positive metal ions are held in a fixed regular arrangement called the lattice and are vibrating about their positions.
3. As the electrons drift they collide with these vibrating positive ions, and every collision transfers energy from the electrons to the ions and slows the electrons down.
4. Resistance is therefore a measure of how often the electrons collide on their way through the material, so more frequent collisions mean a larger resistance.
5. The unit of resistance is the ohm, written $\Omega$, and a component has a resistance of $1\Omega$ when a potential difference of $1V$ across it drives a current of $1A$ through it.
6. A short copper connecting lead has a resistance of a small fraction of an ohm, a filament lamp a few ohms, and the plastic sheath around that lead many millions of ohms, which is why virtually no current passes through the sheath.

The resistance equation

1. The three quantities are linked by $V=IR$, where $V$ is the potential difference across the component in volts, $I$ is the current through it in amperes and $R$ is its resistance in ohms.
2. All three values must belong to the same component, so $V$ is the potential difference measured across it and $I$ is the current measured through it.
3. The rearrangements are $I=\frac{V}{R}$ and $R=\frac{V}{I}$, and the form to choose depends only on which of the three quantities is unknown.
4. Reading the equation in the form $R=\frac{V}{I}$ shows that an ohm is a volt per ampere, so $1\Omega =1{V\; A}^{-1}$.
5. Every value must be converted into volts, amperes and ohms before substitution, so $250mA$ becomes $0.250A$ and $4.7k\Omega$ becomes $4700\Omega$.
6. Quoting the equation before substituting earns credit in its own right, so the equation is written out even when the arithmetic that follows is wrong.

Current and resistance

1. With the potential difference held constant, $I=\frac{V}{R}$ shows that the current is inversely proportional to the resistance.
2. Doubling the resistance therefore halves the current, and tripling the resistance reduces the current to one third of its original value.
3. At a fixed $6.0V$, a resistance of $2.0\Omega$ gives $I=3.0A$, a resistance of $6.0\Omega$ gives $I=1.0A$ and a resistance of $12\Omega$ gives $I=0.50A$.
4. The product $IR$ comes to $6.0V$ in each of those three cases, which is exactly what $V=IR$ says.
5. With the resistance held constant instead, $I=\frac{V}{R}$ shows the current is directly proportional to the potential difference, so doubling the supply potential difference doubles the current.
6. The phrase directly proportional is only justified when two quantities give a straight line through the origin, so it fits $I$ against $V$ at constant resistance but never fits $I$ against $R$, whose graph is a curve.

Measuring resistance

1. Resistance cannot be read straight off a meter, so it is worked out from one pair of readings using $R=\frac{V}{I}$.
2. The circuit is a single loop holding a low-voltage supply, a switch, an ammeter and the component whose resistance is wanted.
3. The ammeter is placed in series with the component, so the current it reads is exactly the current passing through that component.
4. The voltmeter is connected in parallel across the component on its own, so the value it reads is the potential difference across that component and not across the whole circuit.
5. The switch is closed only briefly and both meters are read at the same moment, so the pair of values belongs to the same instant.
6. With readings of $V=4.5V$ and $I=0.30A$, the equation $R=\frac{V}{I}$ gives $R=\frac{4.5}{0.30}=15\Omega$.
7. Repeating the pair of readings and taking a mean reduces the effect of random error, and keeping the current small stops the component warming up and changing its resistance while it is being measured.

Variable resistors

1. A variable resistor holds a length of resistance wire with a sliding contact, and only the part of the wire between that contact and one end terminal is included in the circuit.
2. Moving the slider so that more of the wire is included increases the resistance that the charge has to pass through.
3. The variable resistor sits in series with the rest of the loop, so raising its resistance raises the resistance of the whole loop and lowers the current at every point in it.
4. Moving the slider the other way includes less wire, lowers the resistance and raises the current, which is why a single control can be turned smoothly from one extreme to the other.
5. That is how a variable resistor dims a lamp, sets the speed of a small motor and adjusts the volume of a loudspeaker.
6. In a measuring circuit it provides a whole range of current and potential difference pairs from one fixed supply, and it is set to its largest resistance before the switch is closed so that the first current is small.