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Q.1 Materials which easily allow the passage of electric current are known as ______.

A. Conductors

B. Semi-conductors

C. Insulators

D. Dielectrics

Ans : Conductors

Q.2 A wire of length 2m and another wire of length 5m are made up of the same material and have the same area of cross section, which wire has higher resistance?

A. The 2m wire has higher resistance

B. The value of resistance cannot be determined from the given data

C. Both have equal resistance

D. The 5m wire has higher resistance

Ans : The 5m wire has higher resistance

Q.3 Which of the following statements are true with regard to resistance?

A. Resistance is directly proportional to an area of cross section of the wire

B. Resistance is inversely proportional to the resistivity of the wire

C. Resistance is directly proportional to a length of the wire

D. Resistance is inversely proportional to the length of the wire

Ans : Resistance is directly proportional to a length of the wire

Q.4 A wire having an area of cross section = 10sqm and another wire having an area of cross section= 15sqm, have the same length and are made up of the same material. Which wire has more resistance?

A. The 10sqm wire has higher resistance

B. The value of resistance cannot be determined from the given data

C. Both have equal resistance

D. The 15sqm wire has higher resistance

Ans : The 10sqm wire has higher resistance

Q.5 Which, among the following is a unit for resistivity?

A. ohm/metre²

B. ohm-metre²

C. ohm/metre

D. ohm-metre

Ans : ohm-metre

Explanation: Resistivity = Resistance* Length/area of cross section.
Unit of resistivity = ohm*(m²)/m = ohm-m.

Q.6 A wire has the same resistance as the one given in the figure. Calculate its resistivity if the length of the wire is 10m and its area of cross section is 2m.

A. 8 ohm-metre

B. 8 kiloohm-metre

C. 16 ohm-metre

D. 16 kiloohm-metre

Ans : 8 ohm-metre

Explanation: R=V/I = 200/5 = 40ohm.
Resistivity= Resistance*Area of cross section/ Length of the wire.
Resistivity= 40*2/10= 8 ohm-metre.

Q.7 Calculate the ratio of the resistivity of 2 wires having the same length and same resistance with area of cross section 2m2 and 5m2 respectively.

A. 2:7

B. 7:5

C. 5:7

D. 2:5

Ans : 2:5

Explanation: Resistivity = R*A/L

Q.8 What is the resistivity of Copper?

A. 2.7*10^-8ohm-m

B. 5.35*10^-8ohm-m

C. 1.59*10^-8ohm-m

D. 7.3*10^-8ohm-m

Ans : 1.59*10^-8ohm-m

Q.9 The reciprocal of resistivity is________.

A. Resistance

B. Impedance

C. Conductance

D. Conductivity

Ans : Conductivity

Q.10 Which of the following statements are true with regard to resistivity?

A. Resistance does not depend on the temperature

B. Resistivity depend on area of cross section

C. Resistance depends on the temperature

D. Resistivity depend on the length

Ans : Resistance depends on the temperature

## Resistivity

1. Definition: Resistivity, denoted by the symbol ρ (rho), is a material property that quantifies how strongly a specific material opposes the flow of electric current. It is measured in ohm-meters (Ω·m).
2. Unit of Measurement: The unit of resistivity is the ohm-meter (Ω·m), which is derived from Ohm’s Law (V = I * R) and its rearrangement (R = ρ * (L/A)), where R is resistance, ρ is resistivity, L is length, and A is the cross-sectional area.
3. Influence of Temperature: Resistivity is temperature-dependent. In general, as temperature increases, resistivity tends to increase for conductors and decrease for insulators. This temperature dependence is crucial in the design and operation of electronic devices.
4. Relationship with Resistance: The resistance (R) of a conductor is directly proportional to its resistivity (ρ), length (L), and inversely proportional to its cross-sectional area (A), as expressed by the formula R = ρ * (L/A). This relationship highlights the role of resistivity in determining the resistance of a material.
5. Material Variation: Different materials exhibit distinct resistivity values. Metals, known for their high conductivity, have low resistivity, while insulators, such as rubber or glass, have high resistivity. Semiconductors, like silicon, fall in between.
6. Role in Circuit Design: Resistivity is a crucial parameter in the design of electrical circuits. Engineers consider the resistivity of materials when selecting components to ensure the proper functioning of the circuit and to minimize energy losses as heat.
7. Temperature Coefficient: Materials also have a temperature coefficient of resistivity, indicating the rate at which resistivity changes with temperature. This coefficient is essential for predicting and compensating for temperature-induced variations in electrical systems.
8. Superconductivity: Some materials exhibit superconductivity, a state where resistivity drops to zero at very low temperatures. Superconductors have unique applications in areas like magnetic levitation and high-performance electronics due to their zero resistance.
9. Measuring Resistivity: Various methods, such as the four-point probe technique, are employed to measure resistivity experimentally. These methods are essential for characterizing materials and ensuring their suitability for specific applications.
10. Importance in Materials Science: Resistivity plays a central role in materials science, helping researchers understand the electrical properties of materials and guiding the development of new materials with specific conductivity characteristics.