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Electrical Circuits

Syllabus reference

Unit 1, Topic 3 — 15 hours (including practicals)

Electric current

Electric charge is a fundamental property of matter. The SI unit is the coulomb (C). The charge on a single electron is \(e = -1.6 \times 10^{-19}\) C.

Conventional current flows from positive to negative (the direction a positive charge would move). Electron flow is in the opposite direction.

Key formula

\[ I = \frac{q}{t} \]

where \(I\) = current (A), \(q\) = charge (C), \(t\) = time (s)

Potential difference

Electrical potential difference (voltage) is the work done per unit charge as charge moves between two points in a circuit. EMF (electromotive force) is the potential difference across the terminals of a source when no current flows.

Key formula

\[ V = \frac{W}{q} \]

where \(V\) = potential difference (V), \(W\) = work done (J), \(q\) = charge (C)

Resistance

Resistance is a measure of how much a component opposes the flow of current. An ohmic resistor has a constant resistance (linear V–I graph). A non-ohmic resistor has a resistance that changes with current or voltage.

Ohm's law

\[ V = IR \]

where \(V\) = potential difference (V), \(I\) = current (A), \(R\) = resistance (Ω)

Mandatory practical: Ohmic and non-ohmic resistors

Compare the characteristics of ohmic and non-ohmic resistors experimentally. Interpret graphical representations of V vs I data to find resistance using the gradient and its uncertainty.

Power

Key formulas

\[ P = VI = I^2R = \frac{V^2}{R} \]

where \(P\) = power (W)

Series and parallel

Series circuits

Components connected end-to-end. Current is the same through each component; voltage is shared.

[ R_t = R_1 + R_2 + \cdots + R_n ] [ V_t = V_1 + V_2 + \cdots + V_n ] [ I_t = I_1 = I_2 = \cdots = I_n ]

Parallel circuits

Components connected across the same two points. Voltage is the same across each branch; current is shared.

[ \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n} ] [ V_t = V_1 = V_2 = \cdots = V_n ] [ I_t = I_1 + I_2 + \cdots + I_n ]

Circuit analysis

Worked example: Series–parallel circuit

Question: A circuit has a 12 V battery connected to a 4 Ω resistor in series with two parallel resistors of 6 Ω and 3 Ω. Find the total current.

Solution:

Parallel combination: \(\frac{1}{R_p} = \frac{1}{6} + \frac{1}{3} = \frac{1}{2}\), so \(R_p = 2 \text{ Ω}\)

Total resistance: \(R_t = 4 + 2 = 6 \text{ Ω}\)

Total current: \(I = \frac{V}{R_t} = \frac{12}{6} = 2.0 \text{ A}\)

Power dissipation over resistors in a circuit is calculated using \(P = I^2R\) or \(P = \frac{V^2}{R}\) for each component.

Standard circuit symbols

Construct electrical circuit diagrams using standard symbols for: resistor, voltmeter, ammeter, cell, battery, switch, lamp.

Simulations and videos

PhET Simulations:

Crash Course Physics:

External resources: