LAWS OF RESISTANCE

LAWS OF RESISTANCE

1. On what factors does the resistance of a conductor depend

The resistance of a conductor depends on material, dimensions such as length area of cross-section and temperature.

2. Laws of Resistance:-

Laws of Resistance are:-

The Resistance ‘R’ of a conductor of a given material is directly proportional to its length (l) when temperature T and area of cross-section ‘A’ remains constant i.e.,.
R α l

The resistance of a conductor of a given material is inversely proportional to its area of cross-section (A) when length, l and temperature T remain unchanged i.e.,.

3. Specific Resistance or Resistivity (ρ):-

The specific resistance of a material is defined as the Resistance of its specimen of unit length and unit area of cross-section.

4. Derive the formula for specific resistance
Or
Derive the expression relating ‘R’ and ‘ρ’ of a substance.
Or

According to the laws of Resistance,
1. The resistance ‘R’ is directly proportional to the length of the conductor ‘l’.

2. The Resistance ‘R’ is inversely proportional to the area of cross section ‘A’.

From (1) and (2) we have

Where,
ρ is proportionality constant and is called specific resistance Or Resistivity.

5. Differences between Resistance and Specific resistance or Resistivity

Resistance Specific Resistance or Resistivity
1.  Resistance is the property of  a conductor which opposes the flow of electrons through it. 1.  The specific Resistance of a material is defined as the Resistance of its specimen of unit length and unit area of cross-section.
2.  Unit of Resistance is Ohm (Ω). 2.  Unit of specific Resistance is Ohm metre (Ωm).

6. Write the expression for Resistance and the specific resistance.

7. A bulb in a circuit glows instantaneously as soon as you switch on the power source. Why

A bulb in a circuit glows instantaneously as soon as we switch on the power source because the electric filed travels through the circuit at about the speed of light (3×108 m/s) or (3×1010 m/s).

8. Why are Ohmic conductors also called Linear conductors

For the Ohmic conductors the relation between current ‘i’ and potential difference ‘v’ is linear i.e., graph between ‘v’ and ‘i’ for such conductor is a straight line. Hence they are called ‘Linear Conductors’.

II. Problems:-

1. The Resistance of a manganin wire of 1m length is 5 Ω. Find the Resistance of a wire of 3m length of same material having the same area of cross-section

Given,

2. The Resistance of a Manganin wire of 1mm2 cross-sectional area is 15 Ω. Find the Resistance of Manganin wire of same length but of a cross-section of 3mm2

Given,

3. Calculate the Resistance of 1km long copper wire of diameter 2mm. Given that the Resistivity of copper is 1.7×10-8 Ωm

Given,

4. The Resistance of a Brass wire of length 300m and area of cross-section
3.4×10-6m2 is 6Ω. Find the specific Resistance of the material of the wire

Given,


5. The Resistance of an aluminium wire of 2m length is 7 Ohms. What is the Resistance of a wire of 8m length of the same material and of the same cross-sectional area.

Given,

6. The Resistance of a copper wire of 300cm length and 1mm2 cross-sectional area is 15 Ohms. What is the Resistance of a wire if length and area of cross-section are doubled.

Given,


7. A manganin wire of length 10m has a diameter 1mm. Calculate its Resistance if specific Resistance of Manganin is 4.4×10-9 Ωm.

Given,

8. What is the Resistance of a pure Germanium block of dimensions 50cmx2cmx1cm across its length. The Resistivity of pure germanium is
0.6×10-5Ωm.

Given,

9. The Resistance of a manganin wire is R. What will be its Resistance if length is doubled and area of cross-section is halfed.

Let,