Charge and current
Everything electrical starts with charge. In a metal wire the charge that moves is carried by electrons, which drift along when a battery pushes them. Charge is measured in coulombs (C).
Current is simply the rate at which charge flows past a point: a lot of charge passing quickly means a large current. It is measured in amperes, or amps (A), using an ammeter connected in series.
Here \( I \) is the current in amps, \( Q \) is the charge in coulombs, and \( t \) is the time in seconds. One amp is one coulomb of charge flowing every second.
Conventional current
By convention we draw current flowing from the positive terminal to the negative terminal. The electrons actually drift the other way, but every circuit rule at this level uses the conventional direction, so stick with it.
Potential difference: the push
Charge will not flow on its own; it needs a push. That push is the potential difference (p.d.), also called voltage, supplied by a cell or battery. It measures the energy given to each coulomb of charge.
- Potential difference
- The energy transferred per unit charge between two points in a circuit, measured in volts (V) with a voltmeter connected in parallel across the component. One volt is one joule of energy per coulomb of charge.
Think of a simple circuit as a hill. Potential difference is how steep the hill is, current is how many things roll down it each second, and resistance is the roughness that slows the rolling.
Resistance and Ohm's law
Resistance opposes the flow of current. A thin, long or hot wire resists more; a thick, short, cool one resists less. Resistance is measured in ohms (\( \Omega \)). The link between voltage, current and resistance is one of the most used equations in all of electricity.
Here \( V \) is the potential difference in volts, \( I \) is the current in amps, and \( R \) is the resistance in ohms. For a component at constant temperature, current is proportional to voltage, which is Ohm's law.
A resistor carries a current of 0.5 A when connected to a 6 V supply. What is its resistance?
Where this is assessed
Plotting current against voltage for a resistor and finding \( R \) from the graph is a favourite Criterion B and Criterion C practical. A straight line through the origin is the sign that Ohm's law holds; a filament lamp curves, because it heats up.
Series and parallel circuits
How you connect components changes everything about how current and voltage share out. There are two basic ways.
In a series circuit the components sit one after another on a single loop, so there is only one path. In a parallel circuit the components sit on separate branches, so current has more than one path to choose from. The rules follow directly from that difference.
| Quantity | Series | Parallel |
|---|---|---|
| Current | The same everywhere | Splits between branches, then recombines |
| Potential difference | Shares out, adding to the supply | The same across every branch |
| Total resistance | Adds up: \( R_T = R_1 + R_2 \) | Less than the smallest branch |
This is why home lighting is wired in parallel: each lamp gets the full mains voltage, and switching one off does not break the path for the others. In a series string of old fairy lights, by contrast, one broken bulb stops the lot, because there is only one loop.
Parallel resistance surprises people
Adding a resistor in parallel gives the current an extra path, so the total resistance goes down, not up. The combined resistance of a parallel set is always smaller than the smallest single resistor in it.
Check yourself
Attempt each before checking.
1. A charge of 30 C flows through a lamp in 10 s. What is the current? +
\( I = \dfrac{Q}{t} = \dfrac{30}{10} = \) 3 A.
2. Two 4 Ω resistors are connected in series with a 12 V battery. Find the total resistance and the current. +
In series the resistances add: \( R_T = 4 + 4 = 8\;\Omega \). Then \( I = \dfrac{V}{R} = \dfrac{12}{8} = \) 1.5 A, the same current through both resistors.
3. In a parallel circuit, two branches are connected across a 9 V supply. What is the potential difference across each branch? +
In parallel the potential difference is the same across every branch and equals the supply, so it is 9 V across each branch.
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