Draw and interpret circuit diagrams containing cells, batteries, power supplies, generators, potential dividers, switches, resistors (fixed and variable), heaters, thermistors (NTC only), light-dependent resistors (LDRs), lamps, motors, bells, ammete
4.3.1 Circuit Diagrams and Circuit Components
Learning objectives
- Draw accurate circuit diagrams that include every core IGCSE 0625 component and the required supplementary symbols (diodes, LEDs, fuses, relays, safety symbols).
- Interpret a given diagram – identify each symbol, its polarity or switching state, and predict the overall electrical behaviour (current, voltage, power).
- Apply the fundamental series‑parallel laws, Kirchhoff’s voltage and current laws, and the power‑energy relationships when analysing circuits.
Fundamental circuit laws (quick reference)
- Series circuit: same current flows through each element; total resistance \(R{\text{tot}} = R1+R_2+\dots\).
- Parallel circuit: same potential difference across each branch; total conductance \(G{\text{tot}} = G1+G2+\dots\) where \(G = 1/R\). Hence \(\displaystyle \frac{1}{R{\text{tot}}}= \frac{1}{R1}+ \frac{1}{R2}+ \dots\).
- Kirchhoff’s Voltage Law (KVL): the algebraic sum of all potential differences round any closed loop is zero.
- Kirchhoff’s Current Law (KCL): the algebraic sum of currents entering a junction equals the sum leaving it.
- Power and energy: \(P = VI = I^{2}R = \dfrac{V^{2}}{R}\); \(E = Pt\) (where \(t\) is time in seconds).
Standard symbols (Cambridge‑approved)
| Component | Symbol | Polarity / Connection notes | Governing equation / quantitative behaviour | Typical values / remarks |
|---|---|---|---|---|
| Cell (single) |  | Long line = positive terminal, short line = negative terminal. | Provides a constant emf \(E\). No load current‑voltage equation is required for the symbol itself. | Typical emf: 1.5 V (dry cell), 9 V (rectangular). Internal resistance ≈ 0.1 Ω. |
| Battery (multiple cells in series) |  | Series‑connected cells; terminals marked “+” and “–”. | Emf \(E = nE_{\text{cell}}\) where \(n\) is the number of cells. | Common values: 6 V (four 1.5 V cells), 12 V (eight cells). Internal resistance a few Ω for large batteries. |
| Power supply / Generator (DC or AC) |  | Positive and negative terminals shown; AC symbols may include a tilde (~) inside the circle. | DC: \(V = E\) (adjustable). AC: \(V(t)=V_{\text{peak}}\sin\omega t\). | Adjustable lab supplies: 0–30 V, up to 5 A. Internal resistance < 0.1 Ω. |
| Potential divider (two resistors in series with a tap) |  | Tap taken from the junction of the two resistors. | \(V{\text{tap}} = V{\text{total}}\dfrac{R2}{R1+R2}\). Current \(I = \dfrac{V{\text{total}}}{R1+R2}\). | Typical \(R\) values: 1 kΩ – 1 MΩ. Used for reference voltages (e.g., 5 V from 12 V). |
| Switch (single‑pole, single‑throw) |  | Open symbol shown; a closed switch is drawn with a short diagonal line joining the contacts. | When closed, the switch contributes negligible resistance; when open, it breaks the circuit (infinite resistance). | Mechanical switches: 0.1 Ω closed, > 10 MΩ open. |
| Fixed resistor |  | Connected in any orientation; colour‑code not shown in diagram. | Ohm’s law: \(V = IR\). | Common range: 10 Ω – 10 MΩ. Power rating: 0.25 W, 0.5 W, 1 W. |
| Variable resistor (potentiometer) |  | Wiper (the triangle) taps the resistor at a variable point. | \(R{\text{eq}} = R{\text{min}} + \alpha R_{\text{total}}\) where \(\alpha\) is the wiper position (0 – 1). | Typical total resistance: 1 kΩ – 10 kΩ. Power rating usually 0.25 W. |
| Heater (resistive element) |  | Terminals are not polarised. | Power dissipated \(P = I^{2}R = VI\). Temperature rise ∝ \(P\). | Typical resistance: 5 Ω – 50 Ω; power rating 10 W – 1500 W. |
| Thermistor (NTC) |  | Marked “T” to remind that resistance varies with temperature. | \(R = R_{0}\,e^{-\beta T}\) (approx.) or use the datasheet β‑value. \( \displaystyle \frac{dR}{dT}<0\). | Typical: \(R_{0}=10 kΩ\) at 25 °C, β ≈ 0.04 K⁻¹. |
| Light‑dependent resistor (LDR) |  | Circle with a vertical line denotes a light‑sensitive element. | \(R = R{\text{dark}} \left(\frac{L{0}}{L}\right)^{\gamma}\) (qualitative). Resistance falls as illumination \(L\) increases. | Typical: 1 kΩ (bright) – 1 MΩ (dark). γ ≈ 0.5‑0.8. |
| Lamp (incandescent) |  | Non‑polarised; filament is a resistive element whose resistance rises with temperature. | Power \(P = VI\). Filament resistance roughly doubles when hot. | Typical rating: 5 W – 100 W (≈ 10 V – 240 V). Cold resistance ≈ 1/10 of hot resistance. |
| Motor (DC) |  | Polarity matters – reversing the connections reverses rotation. | Effective voltage \(V{\text{net}} = V{\text{applied}} - E{\text{b}}\) where back‑EMF \(E{\text{b}} = k\omega\). Current \(I = \dfrac{V{\text{net}}}{R{\text{arm}}}\). | Small hobby motors: 3 V – 12 V, armature resistance 5 Ω – 20 Ω. |
| Bell (electromagnet) |  | Coil is polarised; the hammer moves when current flows. | Current creates a magnetic field; the mechanical work is small compared with electrical power input. | Typical coil resistance 10 Ω – 50 Ω, operates from 6 V – 12 V. |
| Ammeter |  | Connected in series; internal resistance ≪ circuit resistance. | Measures current \(I\). No equation needed beyond series connection. | Range: 0‑10 A (typical), 0‑0.1 A for sensitive meters. |
| Voltmeter |  | Connected in parallel; internal resistance ≫ circuit resistance. | Measures potential difference \(V\) across its terminals. | Range: 0‑500 V (typical), 0‑10 V for fine measurements. |
| Magnetising coil (inductor) |  | Polarity not indicated; symbol may be drawn with a dot for the start of the coil. | Induced emf \(V_L = -L\frac{dI}{dt}\). Energy stored \(U = \tfrac12 LI^{2}\). | Typical inductance: 10 mH – 10 H (lab coils). |
| Transformer (ideal) |  | Primary and secondary windings are shown; dots indicate the same polarity ends. | \(\displaystyle \frac{Vs}{Vp} = \frac{Ns}{Np}\), \(\displaystyle \frac{Is}{Ip} = \frac{Np}{Ns}\) (ideal, no losses). | Step‑up or step‑down ratios from 1:1 to 10:1 are common in exam questions. |
| Fuse |  | Placed in series; melts if current exceeds rating. | Current rating \(If\); when \(I > If\) for a short time the fuse opens (infinite resistance). | Typical: 0.5 A, 1 A, 3 A, 5 A. |
| Relay (electromagnetic switch) |  | Coil (left) controls a set of contacts (right). Coil is polarised; contacts may be normally open (NO) or normally closed (NC). | When coil current flows, magnetic force moves contacts, changing the circuit path. | Coil voltage: 5 V‑12 V; contact rating up to several amperes. |
| Diode (supplementary) |  | Triangle points towards the line – arrow indicates forward direction (conventional current flows from anode to cathode). | Ideal I‑V: \(I = 0\) for \(V < 0\); \(I\) unrestricted for \(V \ge 0\). Real diode: \(I = IS\big(e^{V/nVT}-1\big)\). | Silicon diode forward voltage ≈ 0.7 V; reverse breakdown ≈ 50 V – 1000 V. |
| LED (Light‑Emitting Diode) – supplementary |  | Same polarity as a diode; two small arrows indicate light emission. | Forward voltage 1.8 V – 3.3 V depending on colour. I‑V similar to diode, but with a characteristic knee. | Typical current 10 mA – 20 mA; power rating ≈ 20 mW. |
| Earth (ground) symbol – safety |  | Used to show a protective earth connection; always drawn at the low‑potential side of a circuit. | No electrical equation; indicates safety compliance. | Mandatory in all exam diagrams that involve metal enclosures or appliances. |
How to interpret a circuit diagram (step‑by‑step)
- Identify sources and their polarity. Mark the + and – terminals of cells, batteries or power supplies.
- Locate series and parallel groups. Use KVL for each closed loop and KCL at each junction.
- Replace complex symbols with their equations. For example, replace a potential divider with two resistors and apply the divider formula.
- Insert measuring instruments correctly. Ammeter in series, voltmeter in parallel; remember their internal resistances.
- Calculate currents, voltages and power. Start with the simplest loop, solve for unknowns, then work outward.
- Check safety symbols. Ensure fuses, earth connections and relays are placed as shown – they do not affect the ideal calculations but are essential for real‑world design.
Example: Simple lighting circuit
Diagram (text description): A 6 V battery (cell + cell) → switch (open) → series resistor 220 Ω → lamp (30 W) → back to the battery negative terminal. A voltmeter is connected across the lamp.
- When the switch is closed, total series resistance \(R{\text{tot}} = 220 Ω + R{\text{lamp}}\).
- Assuming the lamp operates at its rated power, its hot resistance \(R_{\text{lamp}} = \dfrac{V^{2}}{P} = \dfrac{6^{2}}{30} = 1.2 Ω\).
- Current \(I = \dfrac{6 \text{V}}{220 Ω + 1.2 Ω} \approx 0.027 \text{A}\).
- Voltage across the lamp \(V{\text{lamp}} = I \times R{\text{lamp}} \approx 0.032 \text{V}\) – the lamp will be very dim because the series resistor is far too large.
- The voltmeter reads ≈ 0.03 V, confirming the calculation.
This example illustrates how the symbol table, series‑parallel laws and the power equation combine to predict circuit behaviour.
Key points to remember for the exam
- All symbols must be drawn exactly as in the Cambridge standard – any deviation may lose marks.
- Always show polarity for cells, batteries and diodes/LEDs.
- State the governing equation for each component when you are asked to “explain” the behaviour.
- Use KVL and KCL systematically; they are worth a separate mark in many questions.
- Include safety symbols (fuse, earth, relay contacts) when the question context involves appliances or protective devices.
- When a component is “non‑linear” (lamp, thermistor, LDR, diode) indicate the qualitative trend (e.g., resistance decreases with temperature or light) and, if required, write the appropriate approximate formula.