← All printables Chapter 02 · Electromagnetism · 2 sheets · read the chapter →
Vedatom Physics
FORMULA CARD · PHYSICS.VEDATOM.COM
Chapter 02 · Part V · Electromagnetism
Revised on ____________________
Chapter 02 · Current Electricity

Drift, resistance, and the circuits built on them

2 sheets
2 diagrams
28 results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

Current and resistance

DRIFT IS MILLIMETRES PER SECOND
I.Current  I = dqdt = n A e vd
II.Drift velocity  vd = e E τm ≈ 10−4 m s−1
III.Current density  J = IA = σ E the local form of Ohm's law
IV.Ohm's law  V = I R
V.Resistance  R = ρ LA
VI.Resistivity  ρ = mn e² τ a property of the material
VII.With temperature  ρ = ρ0 (1 + α ΔT) α < 0 for a semiconductor
VIII.Stretched wire  R ∝ L² the volume stays constant
Resistivity belongs to the material; resistance belongs to the specimen. Stretch a wire to twice its length and ρ is unchanged while R quadruples.
II

Networks

SERIES SHARES CURRENT, PARALLEL SHARES VOLTAGE
I.In series  R = R1 + R2
II.In parallel  1R = 1R1 + 1R2
III.Junction rule  Σ I = 0 conservation of charge
IV.Loop rule  Σ ΔV = 0 conservation of energy
V.Power  P = V I = I² R = V²R
VI.Bulbs in series  the largest R is the brightest in parallel, the smallest
PQRSGACBDbalance ⇒ G reads 0, P/Q = R/S
III

Cells and meters

A VOLTMETER READS TERMINAL VOLTAGE
I.Terminal voltage  V = ℰ − I r
II.Maximum power  R = r efficiency then only 50 %
III.Cells in series  ℰ = Σ ℰi , r = Σ ri
IV.Cells in parallel  ℰeq = Σ ℰi/riΣ 1/ri
V.Ammeter  shunt S = Ig GI − Ig in series, low resistance
VI.Voltmeter  R = VIg − G in parallel, high resistance
VII.Wheatstone balance  PQ = RS galvanometer reads zero
VIII.Potentiometer  ℰ1ℰ2 = ℓ1ℓ2 draws no current at balance
IV

Charging and discharging

ONE TIME CONSTANT, τ = RC
I.Charging  q = Q0 (1 − e−t/RC) 63 % at t = τ
II.Discharging  q = Q0 e−t/RC 37 % at t = τ
III.Current  i = ℰR e−t/RC falls either way
IV.Half-life  t = R C ln 2
V.Steady state  a capacitor carries no current treat it as a break
VI.Energy through the resistor  = 12 C ℰ² half the battery's work, always
Electron charge
1.6×10−19 C
Copper, ρ
1.7×10−8 Ω m
Drift speed
≈ 0.1 mm s−1
Signal speed
≈ c
Nichrome, ρ
1.0×10−6 Ω m
1 kWh
3.6×106 J
ℰRCitqchargedischargeQ₀=Cℰone timescale τ = RC governs both
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Confusing resistivity with resistance. Stretching a wire changes R, never ρ.
2Forgetting the internal resistance. A cell's terminal voltage equals its emf only at zero current.
3Putting an ammeter in parallel or a voltmeter in series. Ammeter: series, low R. Voltmeter: parallel, high R.
4Using V = IR across a capacitor branch in the steady state. No current flows there — it is an open circuit.