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3.3 Electric Current, Resistance & Resistor Networks
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1 MCAT Architecture, Test-Day Logistics & Scientific Inquiry Skills
1.1 MCAT Architecture, Test-Day Logistics & Scoring Scale (472–528) 1.2 Scientific Inquiry & Reasoning Skills (SIRS 1–4) & Experimental Design 1.3 Passage Navigation, Section Pacing & Strategic Guessing
2 Physics: Mechanics, Fluids & Periodic Motion
2.1 Translational Kinematics, Projectile Motion & Newton's Laws 2.2 Friction, Centripetal Force & Rotational Equilibrium in Biomechanics 2.3 Mechanical Work, Pressure-Volume Work & Forms of Energy 2.4 The Work-Energy Theorem, Power & Mechanical Advantage 2.5 Hydrostatics, Fluid Dynamics & Circulatory Hemodynamics 2.6 Periodic Motion, Wave Fundamentals, Superposition & Standing Waves 2.7 Sound Intensity, the Decibel Scale & the Doppler Effect
3 Physics: Electromagnetism, Optics & Atomic Physics
3.1 Coulomb's Law, Electric Fields & Electric Potential 3.2 Electric Dipoles, Membrane Potentials & the Nernst Equation 3.3 Electric Current, Resistance & Resistor Networks 3.4 Capacitance, Dielectrics & Axonal Cable Theory 3.5 Light, Refraction, Mirrors & Thin Lenses 3.6 The Optical System of the Eye & Corrective Lens Prescriptions 3.7 Nuclear Architecture, Binding Energy & Radioactive Decay Modes 3.8 Decay Kinetics, Half-Life & Medical Radiation Applications
4 General Chemistry: Atoms, Solutions & Thermodynamics
4.1 Quantum Numbers, Electron Configurations & Periodic Trends 4.2 Lewis Structures, Formal Charge, VSEPR Geometry & Molecular Polarity 4.3 States of Matter, Phase Diagrams, Heating Curves & Solvation 4.4 Concentration Units, Henry's Law & Colligative Properties 4.5 Thermodynamic Systems, the First Law, Enthalpy & Entropy 4.6 Gibbs Free Energy, Equilibrium & Bioenergetic Reaction Coupling 4.7 Collision Theory, Transition States & Empirical Rate Laws 4.8 Integrated Rate Laws, Half-Life, Arrhenius Behaviour & Catalysis
5 General Chemistry: Equilibrium, Acids, Bases & Electrochemistry
5.1 Chemical Equilibrium, Equilibrium Constants & Le Chatelier's Principle 5.2 Acid-Base Definitions, pH Scale, Titrations & Physiological Buffers 5.3 Electrochemical Cells, Reduction Potentials & the Nernst Equation
6 Organic Chemistry: Structure, Stereochemistry & Mechanisms
6.1 IUPAC Nomenclature, Functional Group Priority & Orbital Hybridisation 6.2 Resonance, Inductive Effects & Conformational Analysis 6.3 The Isomer Hierarchy, Chirality & CIP Priority Rules 6.4 Optical Activity, Diastereomers, Meso Compounds & Fischer Projections 6.5 Carbonyl Reactivity: Aldehydes, Ketones & Nucleophilic Additions 6.6 Carboxylic Acids & Derivatives: Nucleophilic Acyl Substitution
7 Bio-Organic Reactions, Laboratory Separations & Spectroscopy
7.1 Alcohol Physical Properties, Acidity, Leaving Groups & Protecting Groups 7.2 Carbon Oxidation States, Laboratory Oxidations & Biological Redox Cofactors 7.3 Extraction, Acid-Base Separation & Distillation 7.4 Analytical and Biomacromolecular Chromatography 7.5 Infrared and UV-Vis Spectroscopy 7.6 1H-NMR, 13C-NMR & Integrated Spectral Elucidation
8 Biochemistry: Amino Acids, Peptides & Enzymes
8.1 Amino Acid Stereochemistry & Side-Chain Classification 8.2 Zwitterions, Titration Curves, Isoelectric Points & the Peptide Bond 8.3 The Hierarchy of Protein Structure 8.4 Folding Thermodynamics, Haemoglobin Cooperativity & Denaturation 8.5 Catalytic Mechanisms, Enzyme Classification & Michaelis-Menten Kinetics 8.6 Enzyme Inhibition Modes & Allosteric Cooperativity
9 Biochemistry: Cellular Metabolism & Bioenergetics
9.1 Glycolysis: The Ten Steps, Regulation & Anaerobic Fermentation 9.2 Gluconeogenesis Bypass Enzymes & the Pentose Phosphate Pathway 9.3 The Pyruvate Dehydrogenase Complex & the Citric Acid (Krebs) Cycle 9.4 Mitochondrial Architecture & the Respiratory Complexes 9.5 Chemiosmotic Coupling, ATP Synthase, NADH Shuttles & Uncouplers 9.6 Fatty Acid Beta-Oxidation, Ketogenesis & Glycogen Dynamics
10 Molecular Biology: Nucleic Acids & Genetic Technologies
10.1 Nucleic Acid Chemistry, the Double Helix & Chromatin Organisation 10.2 DNA Replication: Replisome Enzymology & Fork Dynamics 10.3 DNA Damage & Cellular Repair Pathways 10.4 The Central Dogma, Strand Nomenclature & Transcription Machinery 10.5 Post-Transcriptional Processing of Eukaryotic Pre-mRNA 10.6 Regulation of Gene Expression: Operons, Enhancers & Epigenetics 10.7 The Genetic Code, Wobble & Mutation Taxonomy 10.8 tRNA Charging & the Stages of Ribosomal Translation 10.9 Translation Inhibitors & Post-Translational Processing 10.10 Restriction Enzymes, Cloning Vectors, cDNA Libraries & PCR 10.11 Blotting, Sequencing, Microarrays & CRISPR-Cas9
11 Cellular Biology & Microbiology
11.1 Eukaryotic Organelles, Membrane Transport & Cytoskeletal Dynamics 11.2 The Eukaryotic Cell Cycle, Mitosis, Checkpoints & Apoptosis 11.3 Cell Theory, Bacterial Morphology, Genetics & Sub-Viral Agents
12 Genetics, Evolution & Embryology
12.1 Mendel's Laws & the Cytology of Meiosis 12.2 Genetic Crosses, Non-Mendelian Inheritance, Linkage & Pedigree Analysis 12.3 The Hardy-Weinberg Principle, Assumptions & Clinical Calculations 12.4 Mechanisms of Evolution, Speciation & Macroevolutionary Patterns 12.5 Gametogenesis, Fertilisation, Cleavage & Implantation 12.6 Gastrulation, Germ Layer Derivatives, Stem Cell Potency & Neurulation
13 Human Physiology: Control & Transport Systems
13.1 Neuronal Anatomy, the Resting Potential & the Action Potential 13.2 Conduction Velocity, Synaptic Transmission & Postsynaptic Summation 13.3 Neurotransmitter Systems, CNS/PNS Organisation & Reflex Arcs 13.4 Hormone Classification & the Hypothalamus-Pituitary Axis 13.5 Negative Feedback Architecture, Endocrine Glands & Calcium Homeostasis 13.6 Cardiac Anatomy, Electrophysiology, the Cardiac Cycle & Cardiac Output 13.7 Vascular Hemodynamics, Starling Forces, Blood Components & Hemostasis 13.8 Respiratory Anatomy, Ventilation Mechanics & Pulmonary Surfactant 13.9 Spirometry, Dead Space, Gas Exchange & Haemoglobin Allostery 13.10 Carbon Dioxide Transport, the Chloride Shift & Acid-Base Control of Breathing
14 Human Physiology: Maintenance, Defense & Locomotion
14.1 Renal Anatomy, Glomerular Ultrafiltration & Tubular Transport 14.2 The Countercurrent Multiplier & Endocrine Regulation of Renal Function 14.3 GI Architecture, the Enteric Nervous System & Gastric Secretion 14.4 Pancreatic and Biliary Digestion & Intestinal Nutrient Absorption 14.5 Hepatic Processing, GI Endocrine Regulators & the Colon 14.6 Innate Immunity: Barriers, Complement & Cellular Effectors 14.7 Adaptive Humoral Immunity: B Cells & Immunoglobulins 14.8 Adaptive Cellular Immunity: T Cells, Thymic Selection & MHC Presentation 14.9 Muscle Types, Sarcomere Anatomy & Excitation-Contraction Coupling 14.10 Bone Architecture, Remodelling & the Integumentary System
15 CARS: Passage Analysis & Argument Mapping
15.1 CARS Architecture, Passage Genres (Humanities vs Social Sciences) & Mindset 15.2 Active Reading, Author's Central Thesis & Tone Analysis 15.3 Rhetorical Structure, Claim-Evidence Linkages & Argument Mapping
16 CARS: Question Types & Reasoning Strategies
16.1 Skill 1 Demands, Question Stems, Detail Retrieval & Paraphrase Recognition 16.2 Inferential Meaning, Distractor Taxonomy & a Worked Skill 1 Passage 16.3 Skill 2 Architecture, Question Stems, Unstated Assumptions & Evidence Strength 16.4 Rhetorical Mechanisms, Logical Fallacies & a Worked Skill 2 Passage 16.5 Skill 3 Architecture, Question Stems, Application & Analogy Mapping 16.6 Incorporating New Information, Calibrating Evidentiary Impact & a Worked Skill 3 Passage
17 Sensory Processing, Perception & Cognition
17.1 Sensation versus Perception & Sensory Receptor Classification 17.2 Psychophysical Thresholds, Weber's Law, Adaptation & Signal Detection Theory 17.3 Vision: Ocular Anatomy, Phototransduction & Central Visual Pathways 17.4 Audition & the Vestibular System 17.5 Somatosensation, Pain & Chemoreception 17.6 Models of Attention & Working Memory Architecture 17.7 Long-Term Memory Taxonomy, Encoding, Storage & Retrieval 17.8 Forgetting, Interference, Memory Distortion & Long-Term Potentiation 17.9 Problem Solving, Heuristics, Cognitive Biases & Language 17.10 Sleep Architecture, Circadian Neurobiology, Sleep Disorders & Psychoactive Drugs
18 Emotion, Stress, Motivation & Personality
18.1 Components of Emotion & Classical Theories of Emotion 18.2 The Limbic Circuit, Stress Appraisal & Selye's General Adaptation Syndrome 18.3 Intrinsic and Extrinsic Motivation, Drive-Reduction, Arousal & Incentive Theories 18.4 Cognitive and Humanistic Need Models & the Neuroendocrine Control of Hunger and Sex 18.5 The Psychoanalytic Perspective & Neo-Freudian Revisions 18.6 Humanistic, Trait & Social-Cognitive Perspectives on Personality 18.7 Biopsychosocial Etiology, Schizophrenia, Mood & Anxiety Disorders 18.8 Somatic, Dissociative, Personality & Neurodegenerative Disorders
19 Learning, Social Behavior & Identity
19.1 Non-Associative Learning & Classical Conditioning 19.2 Operant Conditioning, Reinforcement Schedules & Observational Learning 19.3 Self-Concept & Lifespan Developmental Theories 19.4 Kohlberg's Moral Development & Sociocultural Frameworks 19.5 Social Influence: Conformity, Obedience, Group Dynamics & Prosocial Behavior 19.6 Social Cognition, Attribution Theory, Prejudices, Stereotypes & Discrimination
20 Sociology, Demographics & Healthcare Disparities
20.1 Macro versus Micro Paradigms, Structural Functionalism & Conflict Theory 20.2 Symbolic Interactionism, Social Constructionism & Modern Paradigms 20.3 Major Social Institutions: Structure, Function & Dysfunction 20.4 Demographics, Population Pyramids, the Demographic Transition & Globalisation 20.5 Systems of Stratification, Socioeconomic Status & Social Mobility 20.6 Poverty, Spatial Inequality, the Socioeconomic Gradient & Health Inequities
3.3 Electric Current, Resistance & Resistor Networks
Key Takeaways Explain This Topic AI
Current I = Delta Q / Delta t (Amperes) represents net charge flux over time, with conventional current flowing in the direction of positive charge movement.
Conductor resistance R = rho L / A depends on material resistivity rho, length L, and cross-sectional area A; halving axonal radius quadruples internal axoplasmic resistance.
Kirchhoff's junction rule enforces charge conservation (Sum I_in = Sum I_out), while the loop rule enforces energy conservation around closed loops (Sum Delta V = 0).
Last updated: September 2026
3.3 Electric Current, Resistance & Resistor Networks
Note
Bio-Circuit Analogy : On the MCAT, direct-current (DC) electric circuits serve as the primary mathematical model for understanding neural conduction and cardiovascular hemodynamics. The lipid bilayer of a neuron acts as a parallel-plate capacitor, ion channels act as variable resistors, and the concentration gradients generated by metabolic pumps act as chemical batteries.
Electric circuits describe the closed pathways through which electric charges flow under the influence of potential differences. Mastery of circuit theory requires understanding charge conservation, energy conservation, network reduction, and transient charging dynamics.
1. Electric Current, Drift Velocity, and Ohm's Law
Electric current ( I I I ) quantifies the net rate of electric charge transport through a defined cross-sectional boundary: I = Δ Q Δ t I = \frac{\Delta Q}{\Delta t} I = Δ t Δ Q
Units : Amperes ( A \text{A} A ), where 1 A = 1 Coulomb per second 1\text{ A} = 1\text{ Coulomb per second} 1 A = 1 Coulomb per second ( 1 C / s 1\text{ C}/\text{s} 1 C / s ).
Conventional Current vs. Electron Drift : By historical convention established by Benjamin Franklin, current is defined as the direction in which positive charge carriers would flow—from higher electrical potential ( + + + ) toward lower electrical potential ( − - − ). In metallic conductors, mobile charge carriers are negative conduction electrons drifting in the opposite direction.
Ohm's Law
Ohm's law states that for an ohmic conductor, the potential difference ( V V V ) across the component is directly proportional to the current ( I I I ) passing through it: V = I R V = I R V = I R
Where R R R is the electrical resistance, measured in Ohms ( Ω = V / A \Omega = \text{V}/\text{A} Ω = V / A ):
Ohmic Conductors : Exhibit a linear current-voltage relationship ( I I I vs. V V V is a straight line through the origin with slope 1 / R 1/R 1/ R ).
Non-Ohmic Devices : Exhibit nonlinear I I I - V V V curves where resistance varies with applied voltage or current. Biological voltage-gated ion channels, semiconductor diodes, and action potential thresholds are distinctly non-ohmic.
2. Resistance, Resistivity, and Geometric Dependencies
Resistance is an extrinsic property that depends on both the intrinsic material composition and the physical geometry of the conducting pathway: R = ρ L A R = \frac{\rho L}{A} R = A ρ L
Where:
ρ \rho ρ is the resistivity of the material (in Ω ⋅ m \Omega\cdot\text{m} Ω ⋅ m ), reflecting intrinsic resistance to electron passage. Conductivity ( σ \sigma σ ) is the reciprocal of resistivity ( σ = 1 / ρ \sigma = 1/\rho σ = 1/ ρ , in ( Ω ⋅ m ) − 1 (\Omega\cdot\text{m})^{-1} ( Ω ⋅ m ) − 1 or S / m \text{S}/\text{m} S / m ).
L L L is the length of the conductor (in meters). Resistance is directly proportional to length ( R ∝ L R \propto L R ∝ L ); doubling length doubles resistance.
A A A is the cross-sectional area (in m 2 \text{m}^2 m 2 ). Resistance is inversely proportional to area ( R ∝ 1 / A R \propto 1/A R ∝ 1/ A ).
Cylindrical Geometries in Biology
For cylindrical conductors such as blood vessels or neuronal axons with radius r r r (or diameter d = 2 r d = 2r d = 2 r ): A = π r 2 = π d 2 4 ⟹ R = ρ L π r 2 A = \pi r^2 = \frac{\pi d^2}{4} \implies R = \frac{\rho L}{\pi r^2} A = π r 2 = 4 π d 2 ⟹ R = π r 2 ρ L
Important
The Inverse-Square Radius Rule : Because area depends on r 2 r^2 r 2 , halving the radius of an axon increases its internal longitudinal resistance by a factor of 2 2 = 4 2^2 = 4 2 2 = 4 . Conversely, doubling axonal diameter reduces internal resistance to 1 / 4 1/4 1/4 , significantly accelerating passive current propagation.
Temperature Dependence of Resistance
In metallic conductors, electrical resistivity increases with rising temperature ( ρ ( T ) = ρ 0 [ 1 + α ( T − T 0 ) ] \rho(T) = \rho_0[1 + \alpha(T - T_0)] ρ ( T ) = ρ 0 [ 1 + α ( T − T 0 )] ) because thermal lattice vibrations increase the frequency of scattering collisions between conduction electrons and lattice ions.
3. Resistor Networks and Kirchhoff's Laws
Complex circuits can be resolved into equivalent resistances ( R eq R_{\text{eq}} R eq ) using series and parallel combination rules.
Resistors in Series
When resistors are connected end-to-end along a single conducting branch: R eq = R 1 + R 2 + R 3 + ⋯ + R n R_{\text{eq}} = R_1 + R_2 + R_3 + \dots + R_n R eq = R 1 + R 2 + R 3 + ⋯ + R n
Current is Identical : The same current must flow sequentially through every resistor ( I total = I 1 = I 2 = I 3 I_{\text{total}} = I_1 = I_2 = I_3 I total = I 1 = I 2 = I 3 ).
Voltage Divides Additively : The total potential drop across the series chain is the sum of the individual voltage drops ( V total = V 1 + V 2 + V 3 V_{\text{total}} = V_1 + V_2 + V_3 V total = V 1 + V 2 + V 3 ).
Equivalent Resistance Increases : R eq R_{\text{eq}} R eq is always strictly greater than the largest individual resistor in the series combination.
Resistors in Parallel
When resistors are connected across the same two electrical nodes: 1 R eq = 1 R 1 + 1 R 2 + 1 R 3 + ⋯ + 1 R n \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n} R eq 1 = R 1 1 + R 2 1 + R 3 1 + ⋯ + R n 1
For exactly two resistors in parallel, this simplifies to the "product over sum" formula: R eq = R 1 R 2 R 1 + R 2 R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2} R eq = R 1 + R 2 R 1 R 2
Voltage is Identical : The potential difference across each parallel branch is identical ( V total = V 1 = V 2 = V 3 V_{\text{total}} = V_1 = V_2 = V_3 V total = V 1 = V 2 = V 3 ).
Current Divides Inversely : Total current splits among branches, with lower-resistance paths carrying proportionally more current ( I total = I 1 + I 2 + I 3 I_{\text{total}} = I_1 + I_2 + I_3 I total = I 1 + I 2 + I 3 ).
Equivalent Resistance Decreases : Adding another parallel branch provides an additional conductive conduit, always decreasing total R eq R_{\text{eq}} R eq . R eq R_{\text{eq}} R eq is always strictly less than the smallest individual resistor in the parallel group.
Kirchhoff's Circuit Laws
Kirchhoff's Junction Rule (Current Law) : The sum of currents entering any electrical junction must equal the sum of currents leaving that junction: ∑ I in = ∑ I out \sum I_{\text{in}} = \sum I_{\text{out}} ∑ I in = ∑ I out Physical Basis : Conservation of Electric Charge .
Kirchhoff's Loop Rule (Voltage Law) : The algebraic sum of all potential differences around any closed circuit loop is zero: ∑ Δ V = 0 \sum \Delta V = 0 ∑ Δ V = 0 Physical Basis : Conservation of Energy .
Electrical Power and Battery Internal Resistance
Electrical power ( P P P ) dissipated as heat across a resistor or delivered by a source is: P = I V = I 2 R = V 2 R P = I V = I^2 R = \frac{V^2}{R} P = I V = I 2 R = R V 2
Real non-ideal voltage sources possess an internal resistance ( r int r_{\text{int}} r int ). The terminal voltage ( V terminal V_{\text{terminal}} V terminal ) delivered to an external load resistance ( R load R_{\text{load}} R load ) is reduced by the internal voltage drop ( I r int I r_{\text{int}} I r int ): V terminal = E − I r int V_{\text{terminal}} = \mathcal{E} - I r_{\text{int}} V terminal = E − I r int
Where E \mathcal{E} E is the electromotive force (ideal open-circuit voltage).
Series versus Parallel Resistor Behaviour
Passage questions rarely ask for a numerical equivalent resistance without also testing which quantity is shared across the elements. Memorise the sharing rule, not just the formula.
Property Series arrangement Parallel arrangement
Equivalent resistance R e q = R 1 + R 2 + … R_{eq} = R_1 + R_2 + \dots R e q = R 1 + R 2 + … (always larger than the largest element) 1 / R e q = 1 / R 1 + 1 / R 2 + … 1/R_{eq} = 1/R_1 + 1/R_2 + \dots 1/ R e q = 1/ R 1 + 1/ R 2 + … (always smaller than the smallest element)
- Current Identical through every element Divides inversely with resistance
- Voltage Divides in proportion to resistance Identical across every branch
Effect of adding a resistor Total resistance rises, total current falls Total resistance falls, total current rises
Physiological analogue Blood flowing through successive segments of one vessel Blood distributed across parallel capillary beds