Cambridge A-Level Physics 9702 – Resistance and Resistivity
Resistance and Resistivity
Learning Objective
State Ohm’s law and understand the relationship between resistance, resistivity, length and cross‑sectional area of a conductor.
Key Definitions
Resistance (R) : The opposition offered by a material to the flow of electric current. Measured in ohms (Ω).
Resistivity (ρ) : An intrinsic property of a material that quantifies how strongly it resists electric current. Measured in ohm‑metres (Ω·m).
Conductivity (σ) : The reciprocal of resistivity, σ = 1/ρ, measured in siemens per metre (S·m⁻¹).
Ohm’s Law
Ohm’s law relates the potential difference (V) across a conductor to the current (I) flowing through it and its resistance (R):
\$ V = I R \$
In terms of current:
\$ I = \frac{V}{R} \$
Ohm’s law is valid for ohmic conductors where the resistance remains constant over a range of applied voltages.
Resistance of a Uniform Conductor
The resistance of a uniform cylindrical conductor can be expressed using its resistivity:
\$ R = \rho \frac{L}{A} \$
where:
\$\rho\$ = resistivity of the material (Ω·m)
\$L\$ = length of the conductor (m)
\$A\$ = cross‑sectional area (m²)
Factors Affecting Resistance
Material: Different materials have different resistivities.
Length (\$L\$ ): Resistance is directly proportional to length.
Cross‑sectional area (\$A\$ ): Resistance is inversely proportional to area.
Temperature: For most conductors, resistivity increases with temperature; for semiconductors it decreases.
Typical Resistivity \cdot alues
Material
Resistivity (Ω·m)
Copper
1.68 × 10⁻⁸
Aluminium
2.82 × 10⁻⁸
Silver
1.59 × 10⁻⁸
Nickel–Chromium alloy (Nichrome)
1.10 × 10⁻⁶
Glass (dry)
10¹⁰ – 10¹⁴
Example Calculation
Calculate the resistance of a copper wire 2.0 m long with a cross‑sectional area of 0.5 mm².
Given:
\$ \rho_{\text{Cu}} = 1.68 \times 10^{-8}\ \text{Ω·m},\; L = 2.0\ \text{m},\; A = 0.5\ \text{mm}^2 = 0.5 \times 10^{-6}\ \text{m}^2 \$
Using \$R = \rho L / A\$ :
\$ R = \frac{1.68 \times 10^{-8} \times 2.0}{0.5 \times 10^{-6}} = \frac{3.36 \times 10^{-8}}{5.0 \times 10^{-7}} = 0.0672\ \text{Ω} \$
Thus the resistance is approximately \$6.7 \times 10^{-2}\ \text{Ω}\$ .
Suggested Diagram
Suggested diagram: A cylindrical conductor showing length \$L\$ , cross‑sectional area \$A\$ , and the direction of current \$I\$ with voltage \$V\$ applied across its ends.
Summary
Ohm’s law: \$V = IR\$ for ohmic materials.
Resistance depends on material (via resistivity), length, and cross‑sectional area: \$R = \rho L/A\$ .
Resistivity is a fundamental property; lower resistivity means better conductivity.