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Chapter 1 - Electric Current, Ohms Law and Kirchhoffs Laws

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Chapter 2 - Magnetic Effects of Electric Current and Measuring Instruments

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Chapter 3 - Electromagnetic Induction and AC Dynamo and Transformer

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Chapter 4 - Alternating Current AC Circuits

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Chapter 5 - Dual Nature of Wave and Particle

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Chapter 6 - Atomic Spectra and X-Rays

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Chapter 7 - Lasers and Principles

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Chapter 8 - Modern Electronics and Semiconductors

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Text lesson

Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity

Physics

Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity

Overview

Overview

🌳 Concept tree

  • Lesson 1 Electric Current, Potential Difference, Resistance and Resistivity
  • ├── Electric current
  • ├── Potential difference
  • ├── Electromotive force (emf) of a source
  • ├── Resistance and resistivity
  • ├── Ohm's law
  • └── Direction of current
Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 1 / 8
Electric current

Electric current

    • Electric current is the ordered flow of electric charges through a conducting material.
    • In a metal the charge carriers are free electrons; in an electrolyte they are positive and negative ions; in a gas they can be both ions and electrons.
    • Without a potential difference the free electrons of a metal move randomly in all directions, so there is no net flow of charge across any section of the wire.
    • When a source is connected, an electric field is set up along the conductor and the electrons acquire a small, steady drift in the direction opposite to the field, superimposed on their random motion.
    • This ordered drift is the current.

  • Current intensity (I) is the quantity of charge that crosses a section of the conductor each second:

    I = Q / t

    Q is the charge in coulomb (C), t is the time in second (s) and I is in ampere (A). So 1 A = 1 C/s: one ampere is the current when one coulomb of charge passes a section every second.

  • Charge passed in a given time Q = I × t. Always convert minutes or hours into seconds first (1 min = 60 s, 1 h = 3600 s). A very common mistake is to leave the time in minutes.

  • The number of electrons that carry a charge Q is n = Q / e, where e = 1.6 × 10−19 C is the charge of one electron.

  • The current is measured by an ammeter, which is always connected in series in the branch whose current is wanted (it must have a very small resistance so that it does not change the current it measures).

Worked example 1.1.A current of 4.5 A flows through a lamp for 2 minutes. Find the charge that passes and the number of electrons involved.
Step 1t = 2 × 60 = 120 s.
Step 2Q = I t = 4.5 × 120 = 540 C.
Step 3n = Q / e = 540 / (1.6 × 10−19) = 3.375 × 1021 electrons.
Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 2 / 8
Potential difference

Potential difference

  • The potential difference (voltage) between two points is the work done to move one coulomb of charge between them:

    V = W / Q

    W is in joule, Q in coulomb, V in volt, so 1 V = 1 J/C. Two points have a potential difference of one volt when one joule of work is needed to carry one coulomb from one point to the other.

  • It follows that W = V Q = V I t the energy delivered to a part of a circuit equals the voltage across it times the charge that passes through it.
    • Potential difference is measured by a voltmeter, which is always connected in parallel across the two points.
    • It must have a very large resistance so that it takes almost no current from the circuit.
Worked example 1.2.→The work done in moving 8 C of charge between two terminals is 120 J. The potential difference is V = W / Q = 120 / 8 = 15 V. If instead a 6 V battery moves 25 C round a circuit, the energy it supplies is W = V Q = 6 × 25 = 150 J.
Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 3 / 8
Electromotive force (emf) of a source

Electromotive force (emf) of a source

  • The emf of a source (VB) is the total work done to move one coulomb of charge round the whole circuit, both outside the source and inside it. Its unit is also the volt.
  • The emf is a property of the source itself (cell, battery, generator): it tells how much energy the source gives to each coulomb. It is different from the potential difference across the terminals, which is smaller than the emf whenever the source delivers current (see Lesson 3).
  • A way to picture the idea is to think of the source as a pump in a water circuit. The pump gives energy to the water; the pipes (the resistors) waste that energy as friction. The emf is the energy given per coulomb by the "pump"; the potential differences across the resistors are the energy lost per coulomb in each part of the path.
Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 4 / 8
Resistance and resistivity

Resistance and resistivity

  • Resistance

    • (R) is the opposition a conductor offers to the flow of current.
    • Unit: ohm (Ω).
    • One ohm is the resistance of a conductor in which a current of one ampere flows when a potential difference of one volt is applied across its ends.

  • At constant temperature the resistance of a uniform wire depends on:

    1. its length L (R ∝ L): a longer wire means the electrons collide with more atoms on the way,
    2. its cross-sectional area A (R ∝ 1/A): a thicker wire offers more parallel paths,
    3. the material it is made of (through the resistivity ρ).

    Combining the three factors:

    R = ρ L / A

    L in metre, A in m2, R in Ω, so ρ is in Ω·m.

  • Resistivity (ρ) the resistance of a wire of that material of unit length and unit cross-sectional area (a 1 m cube between opposite faces). It depends only on the type of material and the temperature, not on the shape or size of the sample. It is why we can compare materials: silver, copper and aluminium have very small ρ; nichrome and constantan have large ρ; glass and rubber have enormous ρ.
  • Conductivity (σ) is the reciprocal of resistivity σ = 1 / ρ with unit Ω−1·m−1 (siemens per metre). Good conductors have small ρ and large σ; insulators the opposite.

  • For a round wire A = π r2 = π d2 / 4, so doubling the diameter divides the resistance by 4 (same length and material). Reading the formula the other way: a wire with half the diameter has four times the resistance.

    • Resistance is not a property of the material alone (that is ρ).
    • Two copper wires of different length and thickness have different resistances but identical resistivities.

  • If a wire is stretched (or drawn) to a new length, its volume stays constant: L₁A₁ = L₂A₂. So when the length is multiplied by k, the area is divided by k and the resistance is multiplied by k2.

Comparison aspectMain ideaKeywords
Worked example 1.3 (resistivity).
  • A nichrome wire has resistivity 1.1 × 10−6 Ω·m
  • length 5 m and diameter 0.40 mm. Find its resistance
nichromewirelengthdiameter
Step 1radius = 0.20 mm = 2.0 × 10−4 mradius
Step 2A = π r2 = 3.14 × (2.0 × 10−4)2 = 1.257 × 10−7 m2
Step 3R = ρ L / A = 1.1 × 10−6 × 5 / 1.257 × 10−7 = 43.8 Ω
Worked example 1.4 (ratio problem).
  • Wire 1 has length L and diameter d. Wire 2 is made of the same material
  • but its length is 3L and its diameter is d / 2. Find R₂ : R₁
Wirelengthdiametermade
•
  • Same material
  • so ρ is the same
Samematerial
•
  • Area ∝ d2
  • so A₂ = A₁ / 4
Area
•Hence R₂ / R₁ = (L₂ / L₁) × (A₁ / A₂) = 3 × 4 = 12Hence
•So R₂ : R₁ = 12 : 1
Worked example 1.5 (stretching).
  • A wire of resistance 10 Ω is drawn uniformly until its length is doubled. The volume is constant
  • so the area halves and R becomes 10 × 22 = 40 Ω
wireresistancedrawnuniformly
Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 5 / 8
Ohm’s law

Ohm’s law

  • At constant temperature, the current through a conductor is directly proportional to the potential difference across its ends:

    V = I R (R = V / I; on a graph of V against I the slope is R)

    • A conductor that obeys this law (straight V–I line through the origin) is called an ohmic conductor.
    • Metallic wires at constant temperature are ohmic; a lamp filament, a diode and an electrolyte-with-gas tube are not, because their resistance changes as they heat up or as the voltage changes.

  • Ohm’s law has three forms, and you should switch freely between them: I = V / R, V = I R and R = V / I.

    • Why "at constant temperature"?
    • When current flows, the wire heats up, its atoms vibrate more and the collisions of the electrons increase, so the resistance of a metal rises with temperature.
    • A graph of V against I for a long-lasting current in a filament therefore bends upward instead of staying straight.
Worked example 1.6.→An electric kettle element has a resistance of 48 Ω and is connected to a 230 V supply. I = V / R = 230 / 48 = 4.79 A. If a student measures 2.0 A through an unknown resistor under 9.0 V, R = 9 / 2 = 4.5 Ω.
Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 6 / 8
Direction of current

Direction of current

  • By convention (the conventional current) current flows outside the source from the positive terminal to the negative terminal. This is opposite to the actual motion of the free electrons in the metal. Inside the source the conventional current goes from negative to positive, driven by the chemical (or other) energy of the source.
  • All circuit diagrams, and all the sign rules you will use later with Kirchhoff’s laws, use the conventional direction.
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Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 7 / 8
Part 8

Part 8

  • 📖

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

Physics Thanaweya Amma (2026/2027)

  • Lesson 1 – Electric Current, Potential Difference, Resistance and Resistivity
  • Electric current is the continuous flow of free charges through a conducting wire.
  • We analyze current intensity (I = Q/t), potential difference (V = W/Q), electric resistance (R = ρ·L/A), and the physical nature of electrical resistivity (ρ) and conductivity (σ).

🌳 Hierarchy Classification & Concept Tree

Fundamental Electrodynamics

  • ├── 1. Electric Current Intensity (I = Q/t = n·e/t)
  • │ ├── Direction Conventional (Positive to Negative) vs. Actual Electronic (Negative to Positive)
  • │ └── Units Ampere (A) = Coulomb/second (C/s)
  • ├── 2. Potential Difference & Electromotive Force (V = W/Q)
  • │ ├── Work required to transfer unit charge between two points
  • │ └── Battery EMF (VB) Total work done by battery inside and outside the source
└── 3. Electric Resistance & Resistivity
├── Factors affecting resistanceLength (L), Area (A), Temperature (T), Material
├── Resistivity (ρ = R·A/L, unitΩ·m) – Dependent ONLY on material and temperature
└── Electrical Conductivity (σ = 1/ρ, unitΩ−1·m−1 or S/m)

📋 Master Teacher's Blackboard & Exam Secrets

Comparison aspectMain ideaKeywords
RULE 1
  • Resistivity (ρ) and Conductivity (σ) are intrinsic material properties. They DO NOT change when a wire is stretched
  • compressed
  • or cut in half
  • they change ONLY with temperature and type of material
ResistivityConductivityintrinsicmaterial
RULE 2
  • When a wire is stretched or drawn (volume and mass remain constant): If length increases to n times its initial value
  • cross-sectional area decreases to 1/n
  • and its resistance increases by n2 times (R2 / R1 = L22 / L12 = A12 / A22 = r14 / r24)
wirestretcheddrawnvolume
RULE 3Current through an ohmic conductor at constant temperature is directly proportional to the potential difference across its terminals (Ohm's Law: V = I · R)Currentthroughohmicconductor
📊 Comparative AnalysisComparative Analysis: Electrical Parameters and UnitsElectricalParametersUnits
Physical Quantity Symbol & Formula SI Unit & Equivalents Dependence on Wire Dimensions
Electric Current I = Q/t Ampere (A) = C/s Independent (set by V and R)
Potential Difference V = W/Q Volt (V) = J/C Set by external battery / circuit
Resistance R = ρ·L/A Ohm (Ω) = V/A Proportional to L, inversely to A
Resistivity ρ = R·A/L Ohm·meter (Ω·m) Completely INDEPENDENT of L and A
Conductivity σ = 1/ρ Ohm−1·m−1 (S/m) Completely INDEPENDENT of L and A
Lesson 1: Electric Current, Potential Difference, Resistance and Resistivity · 8 / 8