Electric Current, Ohm’s Law and Resistivity — Part 2: Resistance, temperature and power: visual lesson, ISC Class 12 Physics

Lesson

Resistance, temperature and power

Part 2 — how the size of a wire and its temperature set its resistance, and what you pay for when you use electricity.

In this lesson you will

Calculate resistance from resistivity and dimensions; distinguish ohmic from non-ohmic devices
Explain the temperature dependence of resistivity of metals and semiconductors
Calculate electrical power, energy and electricity bills

Diagram

Resistance and resistivity

For a uniform wire: $R = \dfrac{\rho l}{A}$ ρ is the resistivity (Ω m), a property of the material. Conductance $G = 1/R$ (siemens); conductivity $\sigma = 1/\rho$ (S m⁻¹).

Doubling the length doubles R; doubling the area halves R.
Stretching a wire to n times its length (same volume) multiplies R by n².

Worked example

Worked example 3: a heater element

A nichrome wire ( $\rho = 1.1 \times 10^{-6}$ Ω m) is 1.5 m long and 0.30 mm in diameter. Find its resistance.

Step 1 — $A = \pi r^2 = \pi(0.15 \times 10^{-3})^2 \approx 7.07 \times 10^{-8}$ m².
Step 2 — $R = \dfrac{\rho l}{A} = \dfrac{1.1 \times 10^{-6} \times 1.5}{7.07 \times 10^{-8}} \approx 23.3$ Ω.

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