DC Circuits

What you'll learn

DC Circuits form a fundamental component of the CIE IGCSE Physics specification, covering how electrical components behave when connected in series and parallel configurations. This topic requires both conceptual understanding and quantitative problem-solving skills, with exam questions regularly testing circuit analysis, calculations involving current, voltage and resistance, and practical applications. Mastery of DC circuits underpins success in Paper 2 (Core) and Paper 4 (Extended) theory papers, as well as the practical alternative-to-practical papers.

Key terms and definitions

Direct current (DC) — electric current that flows in one direction only, typically supplied by cells or batteries, as opposed to alternating current which periodically reverses direction.

Series circuit — a circuit arrangement where components are connected end-to-end along a single path, so the same current flows through each component in turn.

Parallel circuit — a circuit arrangement where components are connected across the same two points, creating multiple paths for current to flow, each path experiencing the same potential difference.

Electromotive force (e.m.f.) — the energy supplied by a cell or power supply per unit charge passing through it, measured in volts; represents the total voltage supplied before any internal energy losses.

Potential difference (p.d.) — the energy transferred per unit charge between two points in a circuit, measured in volts; also called voltage.

Internal resistance — the resistance within a power supply itself that causes some electrical energy to be dissipated as heat inside the supply, reducing the voltage available to the external circuit.

Terminal potential difference — the voltage measured across the terminals of a power supply when current flows; always less than the e.m.f. due to internal resistance.

Conventional current — the direction of current flow from positive to negative terminal, representing the flow of positive charge (opposite to electron flow direction).

Core concepts

Series circuits: current, voltage and resistance

In a series circuit, components are arranged in a single continuous loop. This configuration produces specific, predictable behaviours that appear frequently in CIE IGCSE exam questions:

Current in series circuits:

• The same current flows through every component
• Current is not "used up" as it passes through components
• Mathematical relationship: I₁ = I₂ = I₃ = ... (for all components)
• Ammeter readings placed anywhere in a series circuit will show identical values

Voltage in series circuits:

• The total voltage supplied by the cell or battery divides between components
• Voltage across each component depends on its resistance
• Mathematical relationship: V_total = V₁ + V₂ + V₃ + ...
• The sum of voltages across all components equals the supply voltage (e.m.f.)
• Components with greater resistance have larger voltage drops across them

Resistance in series circuits:

• Total resistance equals the sum of individual resistances
• Mathematical relationship: R_total = R₁ + R₂ + R₃ + ...
• Adding more components in series increases total circuit resistance
• Increased total resistance decreases the current flowing through the circuit (assuming constant supply voltage)

Parallel circuits: current, voltage and resistance

In a parallel circuit, components are connected across the same two points, creating multiple pathways. Understanding parallel behaviour distinguishes high-achieving students:

Current in parallel circuits:

• Current splits at junctions, dividing between parallel branches
• More current flows through branches with lower resistance
• Mathematical relationship: I_total = I₁ + I₂ + I₃ + ...
• The sum of currents entering a junction equals the sum leaving (conservation of charge)
• Each branch operates independently; changing one branch affects only the current in that branch

Voltage in parallel circuits:

• All components connected in parallel experience the same potential difference
• Mathematical relationship: V₁ = V₂ = V₃ = V_supply
• This is the defining characteristic of parallel connection
• Voltmeter readings across any parallel branch show identical values

Resistance in parallel circuits:

• Total resistance is less than the smallest individual resistance
• Mathematical relationship: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
• For two equal resistors in parallel: R_total = R/2
• Adding more parallel branches decreases total circuit resistance
• Decreased total resistance increases the total current drawn from the supply

Practical applications of series and parallel circuits

Series circuit applications:

• Christmas tree lights (older designs) — if one bulb fails, the entire string goes out because the circuit is broken
• Voltage dividers — used to obtain specific voltages from a higher supply voltage
• Switches controlling an entire circuit — placed in series to control current to all components simultaneously

Parallel circuit applications:

• Domestic household wiring — all appliances receive 230V and operate independently
• Car electrical systems — lights, radio, and other devices function independently; failure of one component doesn't affect others
• Multiple lamps in a room — each can be switched independently while all receive full mains voltage
• Battery packs — cells connected in parallel maintain voltage while increasing capacity and current capability

Cells in series and parallel

Cells in series:

• Total e.m.f. = sum of individual e.m.f.s
• For identical cells: E_total = n × E (where n is number of cells)
• Example: Three 1.5V cells in series provide 4.5V
• Internal resistances also add: r_total = r₁ + r₂ + r₃
• Used when higher voltage is required than a single cell provides

Cells in parallel:

• Total e.m.f. equals the e.m.f. of one cell (assuming identical cells)
• Increases the current capacity and operating time
• Internal resistance decreases: 1/r_total = 1/r₁ + 1/r₂ + ...
• Used when longer battery life is needed at the same voltage

Combined series-parallel circuits

CIE IGCSE Extended tier questions often feature circuits combining both arrangements:

Systematic analysis approach:

1. Identify which components are in series and which are in parallel
2. Calculate equivalent resistance for parallel sections first
3. Combine series resistances to find total circuit resistance
4. Use V = IR to find total current from the supply
5. Work backwards through the circuit using voltage and current rules
6. Check that voltages sum correctly and currents split correctly at junctions

Key strategy: Simplify complex circuits step-by-step, replacing groups of resistors with their equivalent resistance until a single value is obtained.

Internal resistance and terminal potential difference

Real power supplies possess internal resistance (r), which causes the terminal p.d. to be less than the e.m.f. when current flows:

Key relationships:

• Terminal p.d.: V = E - Ir (where E is e.m.f., I is current, r is internal resistance)
• Alternatively: E = I(R + r), where R is external resistance
• When no current flows (open circuit): terminal p.d. equals e.m.f.
• As current increases, terminal p.d. decreases due to voltage lost across internal resistance

Practical implications:

• Old or depleted batteries have higher internal resistance
• When a battery is heavily loaded (large current demand), the terminal voltage drops significantly
• This explains why car headlights dim when the starter motor operates (high current draw)

Using Ohm's law in DC circuits

Ohm's law (V = IR) forms the mathematical foundation for all DC circuit calculations:

Application to series circuits:

• Use R_total = R₁ + R₂ + R₃ to find total resistance
• Calculate total current: I = V_supply / R_total
• Find individual voltages: V₁ = IR₁, V₂ = IR₂, etc.
• Verify: V₁ + V₂ + V₃ should equal V_supply

Application to parallel circuits:

• Calculate 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
• Find total current: I_total = V_supply / R_total
• Since voltage across each branch equals V_supply, find branch currents: I₁ = V/R₁, I₂ = V/R₂
• Verify: I₁ + I₂ + I₃ should equal I_total

Worked examples

Example 1: Series circuit calculation

Question: A 12V battery is connected to three resistors in series: 4Ω, 6Ω and 8Ω. Calculate: (a) the total resistance [1] (b) the current flowing through the circuit [2] (c) the voltage across the 6Ω resistor [2]

Solution:

(a) R_total = R₁ + R₂ + R₃ = 4Ω + 6Ω + 8Ω = 18Ω ✓

(b) Using V = IR, rearranged: I = V / R

I = 12V / 18Ω ✓

I = 0.67A (or 2/3 A) ✓

(c) For the 6Ω resistor: V = IR

V = 0.67A × 6Ω ✓

V = 4.0V ✓

Mark scheme notes: Part (a) awards 1 mark for correct addition. Part (b) awards 1 mark for correct formula/method and 1 mark for answer with correct unit. Part (c) awards 1 mark for using the current calculated in part (b) and 1 mark for correct answer.

Example 2: Parallel circuit calculation

Question: Two resistors, 12Ω and 6Ω, are connected in parallel to a 9V battery. (a) Calculate the total resistance of the circuit [2] (b) Calculate the total current supplied by the battery [2] (c) Calculate the current through the 12Ω resistor [2]

Solution:

(a) Using 1/R_total = 1/R₁ + 1/R₂

1/R_total = 1/12 + 1/6 = 1/12 + 2/12 = 3/12 ✓

R_total = 12/3 = 4Ω ✓

(b) I_total = V / R_total

I_total = 9V / 4Ω ✓

I_total = 2.25A ✓

(c) Voltage across 12Ω resistor = 9V (same as supply in parallel)

I = V / R = 9V / 12Ω ✓

I = 0.75A ✓

Mark scheme notes: Part (a) requires correct reciprocal formula (1 mark) and correct calculation (1 mark). Students often forget to take the reciprocal of their final answer.

Example 3: Internal resistance calculation

Question: A cell has an e.m.f. of 6.0V and internal resistance 0.5Ω. It is connected to a 5.5Ω resistor. (a) Calculate the current in the circuit [2] (b) Calculate the terminal potential difference [2]

Solution:

(a) Total resistance = R + r = 5.5Ω + 0.5Ω = 6.0Ω ✓

I = E / (R + r) = 6.0V / 6.0Ω = 1.0A ✓

(b) Method 1: V = E - Ir = 6.0V - (1.0A × 0.5Ω) = 6.0V - 0.5V = 5.5V ✓✓

Method 2: V = IR = 1.0A × 5.5Ω = 5.5V ✓✓

Mark scheme notes: Alternative methods both valid. Students must show working clearly to gain method marks if final answer is incorrect.

Common mistakes and how to avoid them

• Mistake: Assuming current is "used up" in series circuits, so current decreases through successive components. Correction: Current is the same at all points in a series circuit. Charge is conserved; electrons do not disappear. Energy is transferred by the current, not current itself.

• Mistake: Adding resistances in parallel using R_total = R₁ + R₂ + R₃ (series formula applied incorrectly). Correction: Parallel resistance uses reciprocals: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. Remember that parallel total resistance is always smaller than the smallest individual resistor.

• Mistake: Stating that voltage is the same across all components in series circuits. Correction: In series, voltage divides between components (V_total = V₁ + V₂ + V₃). In parallel, voltage is the same across all branches. These are opposite behaviours that must not be confused.

• Mistake: Forgetting to include internal resistance when calculating circuit current or terminal p.d. Correction: Always add internal resistance to external resistance when finding total circuit resistance: R_total = R_external + r. Check question wording carefully for mention of internal resistance.

• Mistake: Not recognising which components are in series and which are in parallel in combined circuits. Correction: Trace current paths carefully. Components are in series if all current flowing through one must flow through the other. Components are in parallel if they are connected across the same two points.

• Mistake: Confusing e.m.f. with terminal potential difference. Correction: E.m.f. is the total voltage supplied by the cell with no current flowing. Terminal p.d. is the voltage available to the external circuit when current flows, always less than e.m.f. due to internal resistance losses: V = E - Ir.

Exam technique for DC Circuits

• "Calculate" questions require numerical answers with working shown. CIE mark schemes award method marks separately from answer marks, so always show formula selection, substitution of values, and unit in final answer. Typical pattern: 1 mark for correct formula/method, 1 mark for correct answer and unit.

• Circuit diagrams may require you to add ammeters (in series) or voltmeters (in parallel). Extended tier questions ask you to predict readings on meters after changes to circuits. Draw clear circuit symbols using a ruler; incorrect symbols lose marks.

• "Explain" and "describe" questions about series/parallel differences require comparative statements. State both behaviours explicitly: "In series, current is the same through all components, whereas in parallel, current divides between branches." Single-sided answers gain partial marks only.

• Combined calculations in multi-step problems require systematic working through the circuit. Show each calculation stage clearly. If you make an error early, clear working allows you to gain subsequent method marks through error-carried-forward marking.

Quick revision summary

Series circuits: same current throughout; voltages add (V_total = V₁ + V₂); resistances add (R_total = R₁ + R₂). Parallel circuits: same voltage across branches; currents add (I_total = I₁ + I₂); resistances combine using reciprocals (1/R_total = 1/R₁ + 1/R₂). Internal resistance (r) causes terminal p.d. to be less than e.m.f. when current flows: V = E - Ir. Use Ohm's law (V = IR) systematically with appropriate series/parallel rules for all calculations. Practise identifying circuit configurations and simplifying combined circuits step-by-step.