Electric Circuits — Pearson A-Level Physics Revision

    This subtopic explores the behaviour of real power sources by introducing the concept of internal resistance, which causes the terminal potential differenc

    Topic Synopsis

    This subtopic explores the behaviour of real power sources by introducing the concept of internal resistance, which causes the terminal potential difference to be less than the electromotive force (e.m.f.) when a current flows. Students learn to calculate the terminal p.d. using V = ε – Ir and to interpret and analyse linear graphs of terminal p.d. against current to determine both the e.m.f. and internal resistance. These skills are fundamental to evaluating battery performance and energy dissipation in practical circuits.

    Key Concepts & Core Principles

    Exam Tips & Revision Strategies

    Common Misconceptions & Mistakes to Avoid

    Examiner Marking Points

    Electric Circuits

    PEARSON
    A-Level

    This subtopic explores the behaviour of real power sources by introducing the concept of internal resistance, which causes the terminal potential difference to be less than the electromotive force (e.m.f.) when a current flows. Students learn to calculate the terminal p.d. using V = ε – Ir and to interpret and analyse linear graphs of terminal p.d. against current to determine both the e.m.f. and internal resistance. These skills are fundamental to evaluating battery performance and energy dissipation in practical circuits.

    12
    Objectives
    20
    Exam Tips
    20
    Pitfalls
    12
    Key Terms
    26
    Mark Points

    Subtopics in this area

    Electromotive force and internal resistance
    Resistance and resistivity
    Power and EMF
    Current, potential difference and resistance
    Current and voltage
    Series and parallel circuits

    Topic Overview

    Electric Circuits is a core topic in A-Level Physics that explores the behaviour of electrical components and the flow of charge. You'll study how current, voltage, and resistance interact in series and parallel circuits, applying Ohm's law and Kirchhoff's laws to predict and measure circuit behaviour. This topic also covers the characteristics of components like resistors, diodes, and thermistors, and introduces concepts such as electromotive force (e.m.f.) and internal resistance. Understanding electric circuits is essential for grasping how everyday devices work, from simple torches to complex electronic systems.

    This topic builds on GCSE knowledge and deepens your understanding of energy transfer and conservation in electrical systems. You'll learn to analyse circuits using both theoretical calculations and practical experiments, developing skills in data collection, graph plotting, and error analysis. Mastery of electric circuits is crucial for topics like capacitance, alternating current, and even quantum physics, as it provides the foundation for understanding how charges move and interact. In exams, you'll be expected to solve problems involving circuit diagrams, calculate unknown quantities, and explain the behaviour of components under different conditions.

    Key Concepts

    Core ideas you must understand for this topic

    • →Ohm's Law: The current through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant. This is expressed as V = IR.
    • →Kirchhoff's Laws: Kirchhoff's first law (junction rule) states that the total current entering a junction equals the total current leaving it (conservation of charge). Kirchhoff's second law (loop rule) states that the sum of e.m.f.s around any closed loop equals the sum of potential differences (conservation of energy).
    • →Resistors in Series and Parallel: In series, total resistance R_total = R1 + R2 + ...; in parallel, 1/R_total = 1/R1 + 1/R2 + ... . These rules allow calculation of equivalent resistance in complex circuits.
    • →Electromotive Force (e.m.f.) and Internal Resistance: The e.m.f. of a cell is the energy supplied per unit charge, while internal resistance (r) causes a voltage drop inside the cell. The terminal voltage V = ε - Ir, where I is the current.
    • →I-V Characteristics: Components like ohmic conductors (linear), filament lamps (non-linear due to heating), diodes (conduct only in one direction), and thermistors (resistance decreases with temperature) have distinct current-voltage graphs that you must be able to interpret.

    Learning Objectives

    What you need to know and understand

    • Calculate terminal potential difference
    • Determine internal resistance from graphs
    • Calculate resistance using resistivity
    • Analyse series and parallel circuits
    • Calculate electrical power
    • Understand EMF and internal resistance
    • Use Ohm's law and calculate resistance
    • Calculate resistivity of a material
    • Define electric current and potential difference
    • Use Ohm's law and calculate resistance
    • Calculate total resistance in series and parallel
    • Analyse potential divider circuits

    Marking Points

    Key points examiners look for in your answers

    • Award credit for demonstrating correct use of the terminal p.d. equation V = ε – Ir, clearly identifying V, ε, I, and r with appropriate units.
    • Look for the ability to rearrange the equation into the form V = –rI + ε and recognise that a graph of V against I yields the e.m.f. as the y-intercept and the internal resistance as the negative gradient.
    • Credit should be given for accurately determining the gradient from a line of best fit, including the use of a large triangle and correct calculation of rise over run, giving r in ohms.
    • Award marks for correctly interpreting the intercept as the open-circuit voltage (e.m.f.), and for explaining that this is the terminal p.d. when no current flows.
    • Calculate resistance using resistivity formula.
    • Analyse series circuits to find total resistance.
    • Analyse parallel circuits to find total resistance.
    • Explain the relationship between resistance and resistivity.
    • Calculate electrical power using P=IV and related formulas.
    • Explain the concept of EMF and internal resistance.
    • Solve problems involving terminal voltage and load.
    • Applies Ohm's law (V=IR) correctly.
    • Calculates resistance in series and parallel circuits.
    • Uses resistivity formula (R=ρL/A) to find resistivity.
    • Interprets circuit diagrams and experimental data.
    • Define electric current as the rate of flow of charge.
    • Define potential difference as the energy per unit charge.
    • State Ohm's law: V = IR.
    • Calculate resistance using Ohm's law.
    • Describe the relationship between current, voltage, and resistance.
    • Award credit for correctly applying the formula R_total = R1 + R2 + ... for resistors in series.
    • Award credit for correctly applying the formula 1/R_total = 1/R1 + 1/R2 + ... for resistors in parallel, including proper manipulation of reciprocals.
    • Award credit for breaking down a mixed series-parallel circuit into simpler parts and systematically calculating the total resistance.
    • Award credit for deriving or stating the potential divider formula V_out = V_in * (R2 / (R1 + R2)) and applying it correctly.
    • Award credit for explaining how changing one resistor in a potential divider affects the output voltage, e.g., in sensor circuits (LDR, thermistor).
    • Award credit for solving problems involving a variable resistor or potentiometer as a potential divider.

    Examiner Tips

    Expert advice for maximising your marks

    • 💡When asked to determine internal resistance from a graph of terminal p.d. against current, always write down the linear equation V = –rI + ε and identify that the gradient magnitude is r, ensuring you state the calculation clearly.
    • 💡To maximise marks, choose scales for your graph that use at least half the paper and draw a line of best fit—not a dot-to-dot. Use a large triangle to calculate the gradient, showing your working explicitly.
    • 💡In exam questions, pay close attention to the circuit setup: if a voltmeter is placed across the battery terminals, it reads terminal p.d., not e.m.f. (unless current is zero), and then use V = ε – Ir to find internal resistance or predict changes.
    • 💡Always check that your final answers have sensible units (Ω for internal resistance, V for e.m.f.) and that the intercept value from the graph makes sense within the context, e.g., a typical 1.5V cell with internal resistance less than 1Ω.
    • 💡Memorise the resistivity formula R = ρL/A.
    • 💡Practice combining resistors in series and parallel.
    • 💡Check units carefully.
    • 💡Draw circuit diagrams to visualise problems.
    • 💡Check units (watts, volts, amps, ohms).
    • 💡Practice with both series and parallel circuits.
    • 💡Write down formulas before substituting values.
    • 💡Check units and convert if necessary.
    • 💡Draw circuit diagrams to visualise connections.
    • 💡Use the formula triangle for Ohm's law.
    • 💡Show working out in calculations.
    • 💡Remember that current flows from positive to negative.
    • 💡Always redraw complex circuits to clearly identify series and parallel sections before calculating.
    • 💡For potential dividers, remember that V_out is proportional to the resistance across which it is measured; think of it as a ratio.
    • 💡Check your units and significant figures; in A-level physics, final answers should be given to an appropriate number of significant figures, typically matching the data provided.
    • 💡Practice deriving the potential divider formula from Ohm's law and the concept of equal current through series resistors; this helps in understanding, not just memorizing.
    • 💡Always draw and label circuit diagrams clearly. Use standard symbols and show the direction of conventional current (from positive to negative). This helps you apply Kirchhoff's laws correctly and avoid sign errors.
    • 💡When solving circuit problems, start by simplifying resistors in series or parallel step by step. Redraw the circuit after each simplification to avoid confusion. Check your final answer by considering whether it makes physical sense (e.g., total resistance in parallel is less than the smallest resistor).
    • 💡For questions involving internal resistance, remember that the terminal voltage is less than the e.m.f. when current flows. Use the equation V = ε - Ir and be careful with signs when applying Kirchhoff's second law.

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Mistakenly treating e.m.f. and terminal p.d. as interchangeable, especially forgetting that terminal p.d. drops under load due to lost volts across internal resistance.
    • Incorrectly plotting or interpreting the graph by swapping axes (e.g., plotting I against V) leading to confusion in gradient and intercept values.
    • Misinterpreting the gradient sign: often students state that internal resistance equals the gradient directly without noting the negative sign in relation to the equation V = ε – Ir.
    • Failing to read the y-intercept precisely, especially if the line doesn't extend to the current axis, or incorrectly extrapolating.
    • Confusing series and parallel formulas.
    • Forgetting to convert units (e.g., length to metres).
    • Misapplying the formula for resistivity.
    • Confusing EMF with terminal voltage.
    • Forgetting to account for internal resistance in circuits.
    • Mixing up power formulas (P=I²R vs P=V²/R).
    • Mixing up units (volts, amps, ohms).
    • Incorrectly adding resistors in parallel.
    • Forgetting to convert units (e.g., mm² to m²).
    • Confusing current and voltage.
    • Forgetting units (amps, volts, ohms).
    • Misapplying Ohm's law to non-ohmic components.
    • Confusing series and parallel resistance formulas, e.g., using product/sum for series.
    • Forgetting to invert the sum after adding reciprocals in parallel resistance calculations.
    • Misapplying the potential divider formula, such as using R1 in the numerator instead of R2, or incorrectly identifying which resistor the output is taken across.
    • Assuming that resistors in parallel always halve the resistance when they are not equal.
    • Misconception: Current is 'used up' as it flows through a circuit. Correction: Current is the flow of charge; it is conserved in a closed loop. Energy is transferred, but charge is not consumed.
    • Misconception: In a parallel circuit, the current is the same through each branch. Correction: The current splits at junctions; the total current entering a junction equals the sum of currents in each branch, but individual branch currents depend on resistance.
    • Misconception: A voltmeter measures the current flowing through it. Correction: A voltmeter is connected in parallel and measures the potential difference across a component; it should have very high resistance to draw negligible current.

    Frequently Asked Questions

    Common questions students ask about this topic

    Before You Start

    Prior knowledge that will help with this topic

    • •Basic understanding of electric current, potential difference, and resistance from GCSE Physics.
    • •Familiarity with circuit symbols and simple series and parallel circuits.
    • •Ability to rearrange equations and work with fractions and decimals.

    Key Terminology

    Essential terms to know

    • Batteries
    • Internal resistance
    • Resistivity
    • Circuit analysis
    • Power dissipation
    • Batteries
    • Ohm's law
    • Resistivity
    • Circuit basics
    • Ohm's law
    • Circuit analysis
    • Potential dividers

    Likely Command Words

    How questions on this topic are typically asked

    Calculate
    Analyse
    Explain
    Determine
    State
    Find
    Show
    Use
    Define
    Describe

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