Problem 2859 - JEE Physics

Question

The reciprocal of resistivity is called (A) mho-m (B) conductivity (C) retentivity (D) conductance

Step-by-Step Solution

Answer

The reciprocal of resistivity is called (B) conductivity.

Step 1: Understand the concept of resistivity

Resistivity (\( \rho\)) is a property of a material that resists the flow of electric current. It is the measure of how strongly a material opposes the flow of electric current. It is usually represented in ohm-meters (Ω.m).

Step 2: Examine the given options

We have four given options, which are: (A) mho-m (B) conductivity (C) retentivity (D) conductance Now, let's examine each option to see if it represents the reciprocal of resistivity.

Step 3: Analyze Option (A) - mho-m

Mho-m is an obsolete unit of electrical conductance, which was replaced by the SI unit of siemens (S). The term "mho" represents the inverse of "ohm", which is the unit of resistance. However, this option does not directly represent the reciprocal of resistivity.

Step 4: Analyze Option (B) - conductivity

Conductivity (\( \sigma\)) is the property of a material that allows the flow of electric current. It is the measure of how well a material can conduct electric current. Conductivity is the reciprocal of resistivity: \( \sigma = \frac{1}{\rho}\). Therefore, this option is the correct answer.

Step 5: Analyze Options (C) and (D) - retentivity and conductance

Retentivity refers to the ability of a material to retain its magnetism, while conductance refers to the ease with which an electric current can pass through a particular medium. Neither of these terms represent the reciprocal of resistivity; hence, they are not the correct answers. #Conclusion#: After analyzing all the given options, we can conclude that the reciprocal of resistivity is called: (B) conductivity

Key Concepts

Resistivity

Resistivity is a fundamental property of a material that quantifies how strongly it opposes the flow of electric current. It is often denoted by the Greek letter \( \rho \) and is expressed in ohm-meters (Ω·m). Materials with high resistivity do not conduct electricity well, while materials with low resistivity are good conductors.

Key points:

• Resistivity essentially measures how much a material resists the electrical charge going through it.
• It is a critical factor in designing and manufacturing electronic components.
• Understanding resistivity helps in choosing the right materials for electrical wiring and other electrical applications.

To calculate resistivity, you would typically measure how much resistance an electric current faces while traveling through a specific material. This is an important consideration in countless applications, from constructing electrical circuits to developing semiconductor devices.

Electrical Conductance

Electrical conductance is a measure of how easily electricity can flow through a material. It is the reciprocal of electrical resistance. The unit of conductance is the siemens (S), where 1 siemens equals the reciprocal of 1 ohm.

The basic relationship between conductance (G) and resistance (R) is given by:

• \( G = \frac{1}{R} \)

Similarly, the relationship between conductivity (\( \sigma \)) and resistivity (\( \rho \)) of a material is:

• \( \sigma = \frac{1}{\rho} \)

Conductance is often used to discuss how well a material or setup can allow an electric current to pass.

Key points:

• High conductance means low resistance, thus allowing more current to flow.
• Conductance values can help in designing circuits that manage power efficiently.

Whether designing small electronics or large-scale electrical grids, understanding and calculating conductance is crucial.

Ohm's Law

Ohm's Law is one of the most basic and essential principles in the study of electricity and electronics. It describes the relationship between voltage, current, and resistance in an electrical circuit. This principle is formulated as:

• \( V = IR \)

where \( V \) is the voltage (measured in volts), \( I \) is the current (measured in amperes), and \( R \) is the resistance (measured in ohms).

When it comes to practical applications, Ohm's Law allows us to:

• Calculate voltage, current, or resistance if the other two quantities are known.
• Understand how circuits behave and predict changes in circuit parameters.
• Design and troubleshoot circuits effectively by analyzing the impact of varying one parameter.

In essence, Ohm's Law provides a straightforward approach to analyze electric circuits and is fundamental for anyone working with electrical systems.