Question

Match list - I with list - II $$ \begin{array}{|l|l|} \hline \multicolumn{1}{|c|} {\text { List - I }} & \multicolumn{1}{|c|} {\text { List - II }} \\ \hline \text { (1) Joule } & \text { (a) henry } \times \text { ampere/sec } \\\ \hline \text { (2) Watt } & \text { (b) coulomb } \times \text { volt } \\ \hline \text { (3) volt } & \text { (c) meter } \times \text { ohm } \\ \hline \text { (4) Resistivity } & \text { (d) (ampere) }^{2} \times \text { ohm } \\ \hline \end{array} $$ (a) \(b, d, c, a\) (b) \(c, a, b, d\) (c) \(b, d, a, c\) (d) \(b, c, a, d\)

Short answer

The short answer is: \((b, d, c, a)\)

Step-by-step solution

Joule

Joule is the unit of energy or work. We know that energy is the product of power and time, and the unit of power is Watt and time is seconds. Alternatively, we can also express energy as a product of charge and voltage, the unit of charge is Coulomb, and voltage is Volt. Therefore, the unit of Joule can be expressed as Coulomb * Volt. From List II, we can see that it matches with option (b).

Watt

Watt is the unit of power. Power is the rate at which energy is consumed or generated. In other words, Power = Energy per unit time. Considering the energy unit is Joule and time is in seconds, we can express Watt as Joule/second. But, as we know from Step 1, Joule can be replaced with Coulomb * Volt. So, Watt can be expressed as (Coulomb * Volt) / second. From List II, it matches with option (d).

Volt

Volt is the unit of voltage. Voltage can also be defined as the electric potential difference between two points. Knowing Ohm's law, voltage is expressed as the product of current and resistance. Therefore, the unit of voltage in terms of current and resistance is given as Ampere * Ohm. From List II, this matches with option (c).

Resistivity

Resistivity is a property of a material that defines its resistance to electric current flow. Using the units of resistance (Ohm), dimensions of the material (meter), and the definition of resistivity, we can determine that the SI unit of resistivity is Ohm * meter. From List II, it corresponds to option (a). Now that we have matched each concept with its respective units, we can express the final answer as (b, d, c, a), which is option (a) in the multiple-choice answers.

Key concepts

SI Units

In physics, SI Units, or the International System of Units, is the standard for measurement widely used across the globe. They provide a universal language for scientists and engineers to communicate measurements clearly and accurately. The system consists of seven base units that define fundamental physical quantities.

• Meter (m): For measuring length or distance.
• Kilogram (kg): For measuring mass.
• Second (s): For measuring time.
• Ampere (A): For measuring electric current.
• Kelvin (K): For measuring temperature.
• Mole (mol): For measuring the amount of substance.
• Candela (cd): For measuring luminous intensity.

Certain derived units are also commonly used, which are combinations of these base units, such as Joule (energy), Watt (power), and Volt (electric potential). Understanding these units and their relationships is crucial for solving problems in physics and engineering.

Electrical Resistance

Electrical resistance quantifies how strongly a material opposes the flow of electric current. It is a critical concept when studying circuits and electronics, defined by the formula:
\[ R = \frac{V}{I} \]where:

• \( R \) is the resistance measured in Ohms (Ω).
• \( V \) is the voltage measured in Volts (V).
• \( I \) is the current measured in Amperes (A).

Materials with high resistance require more voltage to push the same amount of current through them, compared to materials with low resistance. The concept of resistance is vital for designing and analyzing electrical circuits.

Ohm's Law

Ohm's Law forms the foundation for understanding electric circuits and can be stated as:
\[ V = I \times R \]This equation explains the relationship between the voltage (\( V \)), current (\( I \)), and resistance (\( R \)) in a conductor.

• In simple terms, the voltage across an electrical component is directly proportional to the current flowing through it, with the resistance being the constant of proportionality.
• Ohm's Law is applicable to many, but not all, conducting materials, as some materials do not have a constant resistance.

Understanding Ohm's Law is essential for calculating the electrical parameters of components within a circuit and ensuring efficient and safe design.

Energy and Power

Energy and power play crucial roles in physics and engineering, particularly in electrical systems. Energy is the capacity to perform work, and power is the rate at which energy is transferred or converted.

• Energy is measured in Joules (J), which can be thought of as force applied over a distance or as the result of electrical work done.
• Power is measured in Watts (W) and is defined as:
  \[ P = \frac{E}{t} \]where \( P \) is power, \( E \) is energy, and \( t \) is time in seconds.

In electrical systems, power can also be calculated using:
\[ P = V \times I \]Understanding these concepts is essential for analyzing energy consumption and efficiency in electrical devices and systems.

Electric Potential Difference

Electric potential difference, often referred to as voltage, is a fundamental concept in understanding electricity. It represents the work done to move a unit charge between two points in an electric field.

• Measured in Volts (V), the potential difference determines the energy per charge that is available to drive current through a circuit.
• It is the "push" that causes electric charges to flow, effectively functioning as electrical "pressure."
• To gain a deeper understanding of circuits, one must grasp how voltage interacts with current and resistance according to Ohm's Law.

Voltage is pivotal in ensuring the proper functioning of electronic components and is a critical parameter in circuit design and analysis.