Resistors and Resistivity
~8 min read
- Ohm's law: V = IR. Resistance R = V/I. SI unit: ohm (Ω).
- Resistivity: ρ = RA/L. Property of material. Copper ~1.7×10⁻⁸ Ω·m.
- Series and parallel: Series: R = R₁+R₂+… Parallel: 1/R = 1/R₁+1/R₂+…
Resistance is a wire's resistance to electric flow. CDS/OTA tests Ohm's law, series/parallel combinations, and the difference between resistance and resistivity.
Ohm's Law
- At constant temperature, current through a conductor is directly proportional to voltage across it.
- V = IR. R = resistance, measured in ohms (Ω).
- 1 Ω = 1 V/A.
- Ohmic conductors: metals, follow V = IR linearly.
- Non-ohmic: diodes, transistors, electrolytes — V-I curve not a straight line.
Resistance and Resistivity
- R = ρL/A. Resistance ∝ length, inversely ∝ cross-section.
- ρ = resistivity, an intrinsic property of the material. Unit: Ω·m.
- Conductors have low ρ (Cu 1.7×10⁻⁸ Ω·m, Ag 1.6×10⁻⁸). Insulators have very high ρ (rubber, glass ~10¹⁰-10¹⁶).
- Semiconductors (Si, Ge) lie in between.
- Resistance of metals increases with temperature; resistance of semiconductors and electrolytes decreases with temperature.
- Superconductors: zero resistance below a critical temperature (Hg below 4.2 K).
Series and Parallel
| Property | Series | Parallel |
|---|---|---|
| Current | Same through each | Divides among branches |
| Voltage | Divides across each | Same across each |
| Equivalent R | R = R₁+R₂+R₃ | 1/R = 1/R₁+1/R₂+1/R₃ |
| Used for | Christmas lights, fuses | House wiring (each appliance gets full voltage) |
CDS/OTA PYQ Examples
Q: SI unit of resistance is:
(a) Volt (b) Ampere (c) Ohm (d) Coulomb
Answer: (c) Ohm (Ω) = V/A.
Q: Resistance of a metallic wire depends on:
(a) Length only (b) Cross-section only (c) Material only (d) Length, area and material
Answer: (d) R = ρL/A.
Q: In a parallel combination of two equal resistors R, the equivalent resistance is:
(a) 2R (b) R (c) R/2 (d) R/4
Answer: (c) R/2.
Q: As temperature increases, resistance of a metal:
(a) Decreases (b) Increases (c) First increases then decreases (d) Remains constant
Answer: (b) Increases (lattice vibrations scatter electrons more).
Drill Resistors and Resistivity for CDS/OTA
CDS/OTA-pattern items on Resistors and Resistivity with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
What is the difference between resistance and resistivity?
Resistance R depends on shape (L, A) and material; resistivity ρ depends only on material and temperature. Two wires of the same material can have different R but same ρ.
Why is copper used for electrical wiring?
Low resistivity, good ductility, reasonable cost and chemical stability. Silver is even better but too expensive.
Why are house circuits wired in parallel?
Each appliance receives the full 230 V and can be switched independently. In series, a failure anywhere would cut power to everything.