Electric Circuits: Current, Voltage & Resistance

Circuit Symbols

Every circuit diagram is built from standard symbols. You must recognise and draw these accurately in the exam.

Exam tip An ammeter goes in series (in the line of flow). A voltmeter goes in parallel (across the component). Swapping them is a classic lost mark.

Current as Flow of Charge

Current is the rate of flow of electric charge. In metals the charge carriers are electrons, which flow from the negative to the positive terminal. (By convention, conventional current flows from positive to negative — the opposite direction.)

Current is measured in amperes (A) using an ammeter. Charge is measured in coulombs (C).

$$Q = I\,t$$

where $Q$ is charge in coulombs (C), $I$ is current in amps (A) and $t$ is time in seconds (s).

Key terms Current — the rate of flow of charge, $I = Q/t$, measured in amperes (A).

Charge — a property of particles, measured in coulombs (C). One coulomb passes a point when a current of 1 A flows for 1 second.

Worked example A current of 0.5 A flows through a lamp for 2 minutes. How much charge passes through it?

$t = 2 \times 60 = 120\ \text{s}$

$Q = I\,t = 0.5 \times 120 = 60\ \text{C}$

Potential Difference (Voltage)

Potential difference (p.d.), or voltage, is the energy transferred per unit charge between two points. It is measured in volts (V) with a voltmeter connected across the component.

You can think of p.d. as the "push" that drives current around a circuit. The cell provides p.d.; components such as lamps and resistors use it up by transferring the energy to other forms.

Key terms Potential difference — the energy transferred per coulomb of charge passing between two points, measured in volts (V). $1\ \text{V} = 1\ \text{J/C}$.

Resistance and Ohm's Law

Resistance is a measure of how difficult it is for current to flow. It is measured in ohms (Ω). A high resistance means a small current for a given voltage.

$$V = I\,R$$

where $V$ is potential difference in volts (V), $I$ is current in amps (A) and $R$ is resistance in ohms (Ω).

This relationship lets you calculate any one quantity if you know the other two. Rearranged: $R = V/I$ and $I = V/R$.

Worked example A resistor has 6 V across it and a current of 0.4 A flows through it. Find its resistance.

$R = \dfrac{V}{I} = \dfrac{6}{0.4} = 15\ \Omega$

Worked example A 12 Ω resistor is connected to a 3 V supply. What current flows?

$I = \dfrac{V}{R} = \dfrac{3}{12} = 0.25\ \text{A}$

Watch out Always work in base units: volts, amps and ohms. If a current is given in milliamps (mA), divide by 1000 to convert to amps before using $V = IR$.

Series and Parallel Circuits

Components can be connected in two ways. The rules for how current and voltage behave are completely different in each, so learn them carefully.

Series circuit — components joined end to end in a single loop:

The current is the same at every point in the circuit.
The potential difference is shared between components: $V_{total} = V_1 + V_2 + \dots$

Parallel circuit — components on separate branches:

The potential difference is the same across each branch (equal to the supply p.d.).
The current is shared between the branches: $I_{total} = I_1 + I_2 + \dots$ The current splits at junctions and recombines.

Real world Homes are wired in parallel. Each appliance gets the full mains voltage, and you can switch one off without cutting power to the rest.

Exam tip Remember the pattern: series = same current, shared voltage; parallel = same voltage, shared current.

How Current and Voltage Divide

In a series circuit the larger resistor takes the larger share of the voltage, because $V = IR$ and the current is the same through both. If a 2 Ω and a 4 Ω resistor are in series, the 4 Ω resistor gets twice the p.d. of the 2 Ω one.

In a parallel circuit the voltage is fixed across each branch, so the branch with the smaller resistance carries the larger current ($I = V/R$).

I–V Characteristics

An I–V graph plots current against voltage for a component. Its shape tells you how the resistance behaves.

Resistor (at constant temperature): a straight line through the origin. Current is directly proportional to voltage, so resistance is constant. This component is ohmic — it obeys Ohm's law.

Filament lamp: an S-shaped curve. As current increases, the filament heats up, the metal atoms vibrate more, and resistance increases. The line gets less steep at higher voltages.

Diode: current flows freely in the forward direction only. In reverse, the resistance is very high and almost no current flows (the line stays flat). A diode is used to make current flow one way.

Thermistors and LDRs

A thermistor is a resistor whose resistance changes with temperature. For the common type, as temperature increases, resistance decreases. Thermistors are used in temperature sensors and thermostats.

A light-dependent resistor (LDR) changes resistance with light intensity. As light intensity increases, resistance decreases. LDRs are used in automatic lighting and camera light meters.

Key terms Thermistor — resistance falls as temperature rises.

LDR — resistance falls as light gets brighter.

Investigating Resistance

To find how the resistance of a component varies with voltage, set up a circuit with:

1. A cell and a variable resistor to change the current/voltage.
2. An ammeter in series to measure the current $I$.
3. A voltmeter in parallel across the test component to measure the p.d. $V$.

Adjust the variable resistor to get a series of readings, plot an I–V graph, and calculate resistance from $R = V/I$. For a fair test, take readings quickly so the component does not heat up and change its resistance.

Electrical Energy and Power

Power is the rate at which energy is transferred, measured in watts (W).

$$P = V\,I$$

The energy transferred over time is:

$$E = P\,t$$

where $E$ is energy in joules (J), $P$ is power in watts (W) and $t$ is time in seconds (s).

Worked example A lamp runs at 12 V and draws 2 A. Find its power and the energy used in 5 minutes.

$P = V\,I = 12 \times 2 = 24\ \text{W}$

$t = 5 \times 60 = 300\ \text{s}$

Exam tip Keep your equations straight: $Q = It$ (charge), $V = IR$ (Ohm's law), $P = VI$ (power), $E = Pt$ (energy). Knowing which one to reach for is half the battle.