Charge moving round a circuit carries energy from the supply to the components. The main quantities in this topic are current, potential difference and resistance, together with their behaviour in series and parallel circuits.
Circuit diagrams use agreed symbols so any diagram can be read anywhere. Learn the cell (a long line and a short line), the battery (two or more cells), the plain rectangle of a fixed resistor, the arrowed rectangle of a variable resistor, the circle-and-cross lamp, the switch, the ammeter (A) and the voltmeter (V), plus the diode, LED, thermistor, LDR and fuse.
An ammeter goes in series with the component whose current is being measured, and a voltmeter goes in parallel across it.
Current is the rate of flow of electric charge, measured in amperes. Charge is measured in coulombs, and \(Q = It\): charge flow equals current multiplied by time in seconds.
For a charge to flow there must be a complete closed circuit and a source of potential difference. A larger current means more charge passing a point each second.
Potential difference, measured in volts, is the energy transferred per unit of charge passing: \(E = QV\). One volt means one joule transferred for each coulomb.
It can be thought of as the electrical ‘push’ that drives the current, but the definition above is the one to use. Saying current is 'used up' as it goes round is wrong. Energy is transferred; charge is not consumed.
For many components the current is directly proportional to the potential difference, provided the temperature stays constant. That relationship is \(V = IR\), and a component obeying it is called ohmic.
On an I–V graph an ohmic conductor gives a straight line through the origin. A steeper line means a lower resistance.
Resistance opposes the flow of charge and is measured in ohms. For a fixed potential difference, a higher resistance gives a smaller current.
A longer wire has a greater resistance, and increasing the cross-sectional area of a wire decreases its resistance. Resistance is found experimentally by measuring the current through a component and the potential difference across it, then dividing.
A fixed resistor at constant temperature is ohmic. A filament lamp is not: as the current heats the filament, the resistance rises, so its I–V graph curves over. A diode conducts readily in one direction only, so its graph is flat one side of the origin and rises steeply the other.
A thermistor's resistance falls as it gets hotter, which makes it useful in thermostats. An LDR's resistance falls as the light gets brighter, which makes it useful in switching lights on at dusk.
In series there is a single loop, so if one component breaks the whole circuit stops. Adding resistors in series increases the total resistance, because the charge has to pass through them all: \(R_{total} = R_1 + R_2\).
In parallel there is more than one path. Each branch works independently, so one failing does not stop the others, so household wiring is parallel. Adding resistors in parallel decreases the total resistance, because there are more routes for the charge to take, so the total is always less than the smallest single resistor.
In series the current is the same everywhere, because there is only one path, and the supply potential difference is shared between the components in proportion to their resistances.
In parallel the potential difference is the same across every branch, and the total current is the sum of the branch currents. Adding another branch therefore increases the total current drawn from the supply.
A cell or battery gives direct current: the potential difference is always the same way round, so the charge flows in one direction only.
The mains supply is alternating: the potential difference repeatedly reverses, so the current changes direction. In the UK the mains is about 230 V at a frequency of 50 Hz.
A three-core cable has a live wire (brown) at about 230 V, a neutral wire (blue) near 0 V that completes the circuit, and an earth wire (green and yellow) that carries no current unless there is a fault.
The live wire is dangerous even when the appliance is switched off, because it remains at 230 V relative to earth, so touching it completes a path to earth through you. A fuse melts and breaks the circuit if the current becomes too large; the earth wire carries fault current safely away from a metal casing. A double-insulated appliance has two independent layers of insulation between the live parts and the user, so it needs no earth wire.
Power is the rate of energy transfer. In a circuit \(P = VI\), and substituting \(V = IR\) gives \(P = I^2R\) for a component of resistance \(R\).
The second form explains a great deal. Because power depends on the square of the current, doubling the current in a cable quadruples the heating. The National Grid therefore transmits energy at a very high potential difference, so that a smaller current is needed for a given power.
Energy transferred by an appliance is \(E = Pt\), or equivalently \(E = QV\) using the charge that has flowed.
The amount transferred depends on how long the appliance is on and on its power rating. Many appliances also transfer some energy in unwanted ways, usually by heating the surroundings, though for a heater, heating is the useful output.
The National Grid carries electricity from power stations to consumers. Step-up transformers raise the potential difference to hundreds of thousands of volts for transmission, and step-down transformers reduce it again for safe use.
The reason is efficiency. For a given power, a higher potential difference means a smaller current, and because heating in a cable depends on the square of the current, a smaller current wastes far less energy along the way.
A transformer is treated as 100% efficient, so the power in equals the power out: \(V_p I_p = V_s I_s\).
Combine that with \(P = I^2R\) for the cables and the advantage of high-voltage transmission comes out numerically: raise the voltage by a factor of ten and the current falls by ten, so the power wasted in the cables falls by a hundred.
The potential differences are in the same ratio as the numbers of turns on the two coils: \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\).
More turns on the secondary than the primary makes it a step-up transformer; fewer makes it step-down. The primary and secondary values must be substituted on the correct sides of the equation.
Rubbing two insulators together transfers electrons from one to the other. The material that gains electrons becomes negatively charged and the one that loses them is left positively charged. Only electrons move; protons stay in the nucleus.
Like charges repel and unlike charges attract, and both are non-contact forces. Charge builds up on insulators because it cannot flow through them. On a conductor the charge can move through the material, and if there is a conducting path to earth it flows away.
A charged object is surrounded by an electric field, a region where another charge feels a force. The field is strongest close to the object and gets weaker with distance.
Field lines are drawn pointing away from a positive charge and towards a negative one, showing the direction of the force on a small positive charge placed in the field. A second charged object placed in the field feels a force without anything touching it, which is what the field idea is for.
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