An electric circuit is a closed path along which charge can flow. Understanding potential difference (voltage), current, and how to connect components in series and parallel is essential for all of electricity and magnetism.
7.1 Potential Difference and Current
A battery does work on charges to 'push' them around a circuit. The amount of work done per unit of charge is called POTENTIAL DIFFERENCE or VOLTAGE. It is the 'electrical pressure' that drives charge through the circuit.
Definition
Potential difference (V)
Potential difference is the work done per unit positive charge moved between two points in an electric circuit. In symbols: V = W/Q, where V is measured in volts (V), W in joules (J), and Q in coulombs (C).
Formula
Potential difference
V = potential difference (V), W = work done (J), Q = charge (C)
SI unit: V (volt)
Definition
One coulomb (1 C)
One coulomb is the amount of charge that passes through a cross-section of a conductor when a current of one ampere flows for one second: Q = It. Thus 1 C = 1 A·s.
Definition
Electric current (I)
Electric current is the rate of flow of charge past a given point. In symbols: I = ΔQ/Δt, where I is measured in amperes (A), ΔQ in coulombs (C), and Δt in seconds (s).
Formula
Electric current
I = current (A), ΔQ = charge transferred (C), Δt = time (s)
SI unit: A (ampere)
CONVENTIONAL CURRENT DIRECTION: Conventional current is defined as the direction positive charges would move — from the positive terminal of the battery, through the external circuit, to the negative terminal. In reality, it is ELECTRONS (negative charges) that move through metallic conductors, moving in the OPPOSITE direction. We use conventional current direction in circuit diagrams.
Note
In circuit diagrams, conventional current flows from + to − OUTSIDE the battery (through the external circuit). Electrons actually flow from − to + outside the battery. Both descriptions are valid — they describe the same physical situation.
Worked Example
A battery does 24 J of work to move 4 C of charge through a circuit. Calculate the potential difference across the battery.
Given
- W = 24 J
- Q = 4 C
Find
V = ?
Solution
- 1V = W/Q
- 2V = 24/4
- 3V = 6 V
Worked Example
A current of 3 A flows through a resistor for 5 s. How much charge passes through the resistor?
Given
- I = 3 A
- Δt = 5 s
Find
ΔQ = ?
Solution
- 1I = ΔQ/Δt → ΔQ = I × Δt
- 2ΔQ = 3 × 5 = 15 C
Practice Question
A charge of 60 C passes through a wire in 12 s. (a) Calculate the current. (b) If the potential difference across the wire is 4 V, calculate the work done by the source in moving this charge.
(5 marks)