Question

Write down expressions that define (a) resistivity, (b) conductivity and (c) conductance.

Short answer

(a) \( \rho = \frac{R \cdot A}{L} \), (b) \( \sigma = \frac{1}{\rho} \), (c) \( G = \frac{1}{R} \).

Step-by-step solution

Defining Resistivity

Resistivity is a measure of how strongly a material opposes the flow of electric current. It can be represented by the symbol \( \rho \) and is defined by the formula: \( \rho = \frac{R \cdot A}{L} \). Here, \( R \) is the resistance in ohms, \( A \) is the cross-sectional area in square meters, and \( L \) is the length of the material in meters.

Defining Conductivity

Conductivity is a measure of a material's ability to conduct electric current. It is represented by the symbol \( \sigma \) and is the reciprocal of resistivity, which is given as: \( \sigma = \frac{1}{\rho} \). Thus, conductivity is the efficiency of a material in transporting an electric charge.

Defining Conductance

Conductance is the ability of an object to allow the flow of electric current and is represented by \( G \). The formula for conductance is \( G = \frac{1}{R} \), where \( R \) is the resistance in ohms. It quantifies how easily electricity passes through a component.

Key concepts

Resistivity

Resistivity is an essential property of materials that describes how strongly they resist the flow of electric current. Imagine trying to push water through a pipe—resistivity is like the friction the water faces, only for electricity. It determines the efficiency of a material in obstructing electrical flow. Resistivity is represented by the symbol \( \rho \) and is measured in ohm-meters (Ω⋅m). The formula to calculate resistivity is:\[ \rho = \frac{R \cdot A}{L} \]Where:

• \( R \) is the resistance in ohms.
• \( A \) is the cross-sectional area of the material in square meters (m²).
• \( L \) is the length of the material in meters (m).

Materials with high resistivity are poor conductors, like rubber, while those with low resistivity, such as copper, are excellent conductors. Understanding resistivity is crucial for designing circuits and choosing the right materials for electrical applications.

Conductivity

Conductivity is like the flip side of the resistivity coin. It measures how well a material can conduct an electric current. Think of it as how easily the water flows through that same pipe from earlier.Conductivity is represented by the symbol \( \sigma \) and is expressed in siemens per meter (S/m). It is the reciprocal of resistivity, which gives us:\[ \sigma = \frac{1}{\rho} \]This means:

• If a material has high resistivity, it will have low conductivity.
• Conversely, if a material has low resistivity, it will have high conductivity.

Materials like metals often have high conductivity, making them ideal for wiring and other electrical uses. Conductivity helps us understand and predict how electricity will flow through materials and helps select the best materials for efficient energy use.

Conductance

Conductance is yet another essential concept in understanding electrical properties. It represents how easily electricity can pass through an object. If you consider electricity like water, conductance can be compared to the size of the opening through which the water can flow. A larger opening allows more water to pass, just as a higher conductance means electricity flows more readily.Conductance is expressed by the symbol \( G \) and measured in siemens (S). The formula for conductance is:\[ G = \frac{1}{R} \]Where:

• \( R \) is the resistance measured in ohms.

From this, we learn:

• High resistance results in low conductance.
• Low resistance results in high conductance.

Understanding conductance is vital when designing circuits and components, allowing us to determine how well they will transmit electricity. In circuits, higher conductance translates to better current flow and efficiency.