Question

What is the unit of temperature coefficient of resistance? (A) \(\Omega^{-1}{ }^{\circ} \mathrm{C}\) (B) \(\Omega^{1}{ }^{\circ} \mathrm{C}^{-1}\) (C) \({ }^{\circ} \mathrm{C}^{-1}\) (D) \(\Omega^{0}{ }^{\circ} \mathrm{C}^{-1}\)

Short answer

(B) \(\Omega^{1}{ }^{\circ} \mathrm{C}^{-1}\)

Step-by-step solution

Option A: \(\Omega^{-1}{ }^{\circ} \mathrm{C}\)

This option has the inverse of ohms multiplied by degrees Celsius. This does not represent a ratio between resistance and temperature, so this option is incorrect.

Option B: \(\Omega^{1}{ }^{\circ} \mathrm{C}^{-1}\)

This option has ohms divided by the inverse of degrees Celsius. This represents a ratio between resistance and temperature, so this option is correct.

Option C: \({ }^{\circ} \mathrm{C}^{-1}\)

This option only has the inverse of degrees Celsius, without any unit of resistance. It doesn't represent a ratio between resistance and temperature, so this option is incorrect.

Option D: \(\Omega^{0}{ }^{\circ} \mathrm{C}^{-1}\)

This option results in ohms raised to the power of zero, which simplifies to 1. So we are left with the inverse of degrees Celsius, and there is no unit of resistance present. This doesn't represent a ratio between resistance and temperature, so this option is incorrect. After our analysis, the correct unit for the temperature coefficient of resistance is:

Answer:

(B) \(\Omega^{1}{ }^{\circ} \mathrm{C}^{-1}\)

Key concepts

Units of Measurement

The temperature coefficient of resistance is an important concept for understanding how resistance in materials changes with temperature. To effectively measure this relationship, a specific unit is needed. This is expressed as ohms per degree Celsius, represented by the symbol \( \Omega^{1}{ }^{\circ} \mathrm{C}^{-1} \). This unit captures how much the resistance changes per degree of temperature change.

This notation indicates that as temperature increases by one degree Celsius, the resistance changes by a certain amount, measured in ohms. It is crucial to use these units correctly to ensure precise communication of how temperature impacts resistance in materials.

Resistance and Temperature Relationship

Materials typically exhibit a change in resistance when their temperature changes. This relationship is captured by the temperature coefficient of resistance, which quantifies how much resistance varies with temperature. Understanding this concept helps predict and adjust for resistance changes in real-world applications, like in electronic circuits.

Often, the temperature coefficient is positive for conductors, meaning resistance increases with temperature. For semiconductors, it might be negative, signifying a resistance decrease with increasing temperature. This information is important for design and testing, ensuring that components function correctly under varying temperatures.

Ohm's Law

Ohm’s Law is a fundamental principle in electronics that defines the relationship between voltage, current, and resistance in an electrical circuit. It is expressed with the equation \( V = IR \), where \( V \) stands for voltage in volts, \( I \) represents current in amperes, and \( R \) is resistance in ohms. This law is key to understanding how different factors in an electric circuit interact.

By knowing Ohm's Law, we can use the temperature coefficient of resistance in practical applications. For example, changes in resistance due to temperature variations can affect the current and voltage in circuits, and by applying Ohm's Law, these variations can be accounted for and managed.

Physical Constants

Physical constants are fixed values that describe specific physical properties, such as the speed of light or gravitational constant. Within the context of resistance and temperature, these constants include the temperature coefficient of resistance itself. It serves as a parameter that remains constant for a given material under standard conditions.

Knowing the temperature coefficient allows engineers and scientists to predict how a material’s resistance will change with temperature, without needing direct recalculation each time, streamlining processes in design and analysis.

Being familiar with these constants helps improve the reliability of electrical designs, ensuring stability across different environmental conditions.