The Electric River

NODE 01

Idea of Current

• Charge flow as a rate (I = Q/t).
• SI unit: ampere (A).

NODE 02

Conv vs Electron

• Electrons carry charge in metals.
• Electron drift is OPPOSITE to conventional current.

NODE 03

Drift of Carriers

• Random thermal motion + E-field.
• Small average directed motion = drift velocity.

NODE 04

Current Density

• Current per cross-sectional area (J = I/A).
• Vector quantity.

NODE 05

Why Metals Conduct

• Free electrons + Lattice ions.
• EM response propagates near light speed.
• Individual drift is very slow.

NODE 06

Electric Circuit

• Source + Conducting path + Load + Switch.
• Closed vs Open circuit.

NODE 07

Potential Diff

• Voltage represents electric potential diff.
• Energy per unit charge. Voltage drop/rise.

NODE 08

EMF

• Electromotive force. Provides energy to charges.
• EMF is NOT a force; unit is volt.

NODE 09

Cells & Batteries

• Chem energy → electrical energy.
• DC output. Rechargeable vs Non-rechargeable.

NODE 10

Resistance (R)

• Opposes current (R = V/I). Unit: ohm (Ω).
• Depends on material, geometry, temp.

NODE 11

Ohm's Law

V=IR

• V ∝ I (for constant R).
• Empirical relationship, not universal.
• Ohmic vs non-ohmic behaviour.

NODE 12

Resistivity (ρ)

R = ρ

LA

• R = ρL/A. Material property.
• SI unit: Ω·m.

NODE 13

Conductivity (σ)

σ= 1/ρ

• Reciprocal of resistivity.
• Conductors, Semiconductors, Insulators.

NODE 14

Factors affecting R

L

A

MAT

TEMP

• L ↑ → R ↑. A ↑ → R ↓.
• Different materials & temperatures change R.

NODE 15

Temp Dependence

• R ≈ R₀[1 + α(T - T₀)].
• Metals vs Thermistors. Links to thermal Physics.

NODE 16

Series Circuits

• Same current, Voltage division.
• Req = R₁ + R₂ + ...

NODE 17

Parallel Circuits

• Same voltage, Current division.
• 1/Req = 1/R₁ + 1/R₂ + ...

NODE 18

Ser vs Par Map

SER: I=C, V=DIVPAR: V=C, I=DIV

• Series: One break interrupts path.
• Parallel: Other branches may continue.

NODE 19

Kirchhoff Current

• At a junction: ΣI_in = ΣI_out.
• Conservation of Charge.

NODE 20

Kirchhoff Voltage

• Around closed loop: ΣΔV = 0.
• Conservation of Energy. Voltage drops/rises.

NODE 21

Circuit Solving

• Draw → Assign I → Mark Polarities.
• Junction Eqs → Loop Eqs → Solve.

NODE 22

Internal Resistance

• Real cell has internal resistance (r).
• Terminal voltage: V = E - Ir.

NODE 23

Cells in Series

• EMFs can combine (Voltage addition).
• Same current path. Internal res adds.

NODE 24

Cells in Parallel

• Current-sharing.
• Unequal-voltage sources should NOT simply be paralleled.

NODE 25

Electrical Power

P=VI

• P = VI. Also: P = I²R and P = V²/R.
• Power delivered or dissipated.

NODE 26

Electrical Energy

E=Pt

• Energy transferred: E = Pt = VIt.
• Resistor: E = I²Rt. Connects to Realm 06.

NODE 27

Joule Heating

• H = I²Rt. Elec energy → Thermal energy.
• Heaters, toasters, kettles, fuses.

NODE 28

Fuses

• Protects circuit by melting (Joule heating).
• When current exceeds threshold.

NODE 29

Circuit Protection

• Fuse, Circuit breaker.
• Overcurrent, Short circuit, Overload.

NODE 30

Ammeter

• Measures current. Placed in SERIES.
• Ideal ammeter = zero resistance.

NODE 31

Voltmeter

• Measures potential diff. Placed in PARALLEL.
• Ideal voltmeter = infinite resistance.

NODE 32

Galvanometer

• Sensitive current detection.
• Can convert to Ammeter/Voltmeter.
• Realm 18 preview.

NODE 33

Wheatstone Bridge

• Bridge circuit to determine unknown R.
• Balance condition: P/Q = R/S. Null measurement.

NODE 34

Meter Bridge

• Practical extension of Wheatstone.
• Uniform resistance wire, balance point, length ratio.

NODE 35

Potentiometer

• Comparing potential diffs via potential gradient.
• Null method. Compare EMFs / Internal res.

NODE 36

Resistor Networks

• Series-parallel combinations, Symmetry.
• Reduction methods, network reasoning.

NODE 37

Current Division

• Parallel: Current divides by branch resistance.
• I₁/I₂ = R₂/R₁. Lower R gets more I.

NODE 38

Voltage Division

• Series: Voltage divides by resistance.
• Vout = Vin × R₂/(R₁ + R₂).

NODE 39

Short Circuit

• Very low-resistance path → very large current.
• R approaches 0. Heating, protection needed.

NODE 40

Open Circuit

• Broken/incomplete path. Ideal I = 0.
• Potential differences can still exist.

NODE 41

Fault Finding

• No current? Open path, bad source/switch.
• Excess current? Short circuit, excessive load.

NODE 42

Safety (Physics)

• Current through body depends on path impedance.
• Earthing, insulation, dry/wet conditions.

NODE 43

DC Circuits

• Direct Current. Steady flow from DC source.
• Central world of Realm 16. Base for AC.

NODE 44

Transients Preview

• Circuits with energy-storage (Capacitor/Inductor).
• Don't respond instantly. Charging, RC time const.

NODE 45

Exp Lab

ΩV/IρKCLW.B.

• Verify Ohm's law, determine R, ρ.
• Series/Parallel R, internal r, Meter bridge.

NODE 46

Graph Chamber

• V vs I (Slope = R). R vs L. R vs 1/A.
• Energy vs time. Cell V vs I.

NODE 47

Misconceptions

• "Current used up" → No, energy transferred.
• "Voltage flows" → No, charge flows.
• "Ammeter in parallel" → No, series.

NODE 48

Solving Engine

• Draw → ID Source → Label Nodes → Assign I.
• Simplify Ser/Par → Kirchhoff → Ohm's Law.

NODE 49

Master Map

CHARGE → CURRENT → DENSITYVOLT → EMF → RESIST → OHMCIRCUIT → KCL/KVL → POWER

• The entire realm compressed.

NODE 50

Deep Synthesis

E-STATICSE-DYNAMICS

• R15: Charge at rest (Electrostatics).
• R16: Charge in motion (Electrodynamics).
• Moving charge generates magnetic effects...