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Lesson 3, Topic 1
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# Factors Affecting Electrical Resistance of a Conductor

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The electrical resistance of a conductor is affected by the following factors:

1. Temperature: The resistance of a conductor increases as the temperature of the conductor increases i.e. $$\scriptsize R \propto T$$
2. Length: The resistance of a conductor is directly proportional to the length; as the length of a conductor increases, the resistance also increases i.e. $$\scriptsize R \propto L$$
3. Cross sectional Area: The resistance of a conductor increases as the area of the conductor decreases, which reveals that resistance of a wire or a conductor is inversely proportional to the area. $$\scriptsize R \propto \normalsize \frac{1}{A}$$
4. The Nature: The nature of materials of the conductor also affects the resistance of a conductor. Combining all factors, it shows that resistance is directly proportional to length of a conductor and inversely proportional to the area.
$$\scriptsize R \propto \normalsize \frac{L}{A}$$

∴ $$\scriptsize R = \normalsize \frac{\rho L}{A}$$

$$\scriptsize \rho$$ = a constant called resistivity of a materia

∴ $$\scriptsize \rho = \normalsize \frac{RA}{L}$$

Its unit is Ωm-1

Example

Calculate the resistivity of a wire of length 5m of cross sectional area 1.4×10-6m2, its resistance is 3.0Ω

Solution

$$\scriptsize R = \normalsize \frac{\rho L}{A}$$

$$\scriptsize \rho = \normalsize \frac{RA}{L}$$

= $$\frac{3.0 \; \times \; 1.4 \times 10^{-6}}{5}$$

= $$\frac{0.0000042}{5}$$

= 0.00000084

= 8.4 X 10-7Ωm-1

Resistivity is the resistance per unit length of a conductor of unit cross sectional area.

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