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Electric circuits are at the heart of modern technology. Every phone, computer, car, and medical device relies on the controlled flow of electric charge through circuits. Before you can analyse any circuit, you need to understand three foundational quantities: charge, current, and potential difference. These definitions underpin every equation and every circuit calculation at A-Level.
All matter is made of atoms, and atoms contain charged particles. Protons carry a positive charge and electrons carry a negative charge. The fundamental unit of charge is the coulomb (C).
The charge on a single electron is extremely small:
e = 1.60 × 10⁻¹⁹ C
This means that one coulomb of charge is equivalent to roughly 6.25 × 10¹⁸ electrons. In everyday circuits, we routinely deal with charges of several coulombs flowing every second.
Charge is quantised — it always comes in whole-number multiples of the elementary charge e. You cannot have half an electron's worth of charge. This quantisation was demonstrated experimentally by Robert Millikan in his famous oil drop experiment.
Charge is a conserved quantity. It cannot be created or destroyed — it can only be transferred from one place to another. This principle underpins Kirchhoff's first law, which you will meet in a later lesson. At every junction in every circuit, the total charge entering per second must equal the total charge leaving per second.
Current is the rate of flow of electric charge past a point in a circuit. It is defined mathematically as:
I = Q / t
Or equivalently:
Q = It
where:
One ampere means one coulomb of charge flows past a point every second.
A current of 3.0 A flows through a lamp for 2.0 minutes. Calculate the total charge that flows.
Solution:
A current of 0.15 A flows through a thin wire for 30 s. Calculate (a) the total charge that passes and (b) the number of electrons that flow past a point.
Solution:
In a cathode ray tube, 5.0 × 10¹⁵ electrons strike the screen every second. What is the current?
Solution:
Historically, current was defined as the flow of positive charge from the positive terminal of a battery to the negative terminal. This convention was established before anyone knew that in metallic conductors it is actually the negatively charged electrons that move — and they move in the opposite direction, from negative to positive.
We still use the conventional current direction in circuit analysis. This is important to remember: conventional current flows from positive to negative, but electrons flow from negative to positive.
In electrolytes (solutions containing ions), both positive and negative charge carriers can move. Positive ions move in the direction of conventional current, and negative ions move in the opposite direction.
| Material | Charge Carriers | Typical Current Mechanism |
|---|---|---|
| Metals | Free (delocalised) electrons | Drift through lattice of positive ions |
| Electrolytes | Positive and negative ions | Migration under electric field |
| Semiconductors | Electrons and holes | Movement through crystal lattice |
| Gases (ionised) | Electrons and positive ions | Discharge through gas |
Potential difference (p.d.) — often called voltage — is defined as the energy transferred per unit charge as charge moves between two points:
V = W / Q
where:
One volt means one joule of energy is transferred for every coulomb of charge that passes. The volt is therefore equivalent to J C⁻¹.
A 12 V battery drives 5.0 C of charge around a circuit. How much energy is transferred by the battery?
Solution:
A battery of p.d. 9.0 V drives a current of 0.40 A through a resistor for 5.0 minutes. Calculate (a) the total charge that flows, and (b) the total energy transferred to the resistor.
Solution:
The battery (or power supply) is an energy source. It does work on the charge carriers, giving them electrical potential energy. As charge carriers move through components in the circuit, they transfer this energy to other forms:
The key principle is that energy is conserved around any closed loop. The total energy given to the charges by the battery equals the total energy transferred by the charges to the components. This is the basis of Kirchhoff's second law.
flowchart LR
A[Battery] -->|Provides energy to charges| B[Charge carriers gain electrical PE]
B -->|Flow through circuit| C{Components}
C -->|Resistor| D[Thermal energy]
C -->|Lamp| E[Light + heat]
C -->|Motor| F[Kinetic energy]
C -->|Speaker| G[Sound energy]
D --> H[Energy conserved around loop]
E --> H
F --> H
G --> H
Ammeters measure current and must be connected in series — the current you want to measure must flow through the ammeter. An ideal ammeter has zero resistance so it does not affect the circuit.
Voltmeters measure potential difference and must be connected in parallel across the component — they measure the difference in energy per unit charge between two points. An ideal voltmeter has infinite resistance so it draws no current from the circuit.
| Instrument | Connection | Ideal Resistance | Why? |
|---|---|---|---|
| Ammeter | Series | Zero | Must not impede current flow |
| Voltmeter | Parallel | Infinite | Must not draw current from circuit |
Common exam mistake: Confusing the connection requirements. Remember — an ammeter in parallel would short-circuit the component (because it has near-zero resistance). A voltmeter in series would block the current (because it has very high resistance).
These three quantities are deeply interconnected. Current tells you how fast charge is flowing. Potential difference tells you how much energy each unit of charge transfers. Together, they determine the power delivered to or by a component (which you will explore in a later lesson on electrical energy and power).
| Relationship | Equation | Use When You Know |
|---|---|---|
| Charge and current | Q = It | Current and time |
| P.d. and energy | V = W/Q | Energy and charge |
| Combined | W = VIt | Voltage, current, and time |
An LED draws a current of 20 mA from a 3.0 V supply. In one hour of operation, calculate (a) the charge that flows and (b) the total energy transferred.
Solution:
Understanding these definitions precisely is essential because every circuit calculation you perform at A-Level builds on them. When you see V = IR or P = IV, remember that these are consequences of the fundamental definitions of charge, current, and potential difference.