Electrical Circuit Elements: Resistance

Electrical Circuit Elements: Resistance

1. What Resistance Is

Resistance ($R$, ohm $Ω$) = opposition to current flow due to collisions of electrons with lattice. Defined by Ohm's law $V = I R$ for linear $R$ (voltage drop proportional to current). Power dissipated

as heat (Joule heating).

2. Nature — Passive Linear Bilateral

• Passive: absorbs power (cannot generate); active elements (source) deliver.
• Linear: $V∝i$ if $R$ constant (metal at constant $T$); non-linear $R$ varies with $V/I$ (diode, filament hot).
• Bilateral: $V/I$ same both directions (resistor); unilateral (diode) not.

3. Factors

where $ρ$ = resistivity ($Ω·m$, $1.68e-8$ for Cu, $2.8e-8$ for Al), $l$ = length, $A$ = cross-section. Temperature: metals $R$ ↑ with $T$ ($α≈0.004/°C$ for Cu):

Carbon/semiconductor $R$ ↓ with $T$.

Fixed: carbon film, metal film (Ω–MΩ); Variable: rheostat (wire), potentiometer (voltage divider); Thermistor (NTC/PTC), LDR (light)
Symbol: —[R]— or zigzag
Series: R_eq = Σ R_i ; Parallel: 1/R_eq = Σ 1/R_i

6. Exam Points

• Define $R$, $Ω$, $V=IR$, $P=I²R$ — 3-5 marks, very frequent.
• Show $R=ρl/A$ and $R_T$ formula — 5 marks, frequent.
• Series/parallel $R_{eq}$ — 5 marks, very frequent (numerical).
• Linear vs non-linear, active vs passive — 3-5 marks, frequent.