Understanding the Relation Between Volt, Joule, and Coulomb

The question asks about the relationship between Volt (V) and Joule (J). This relationship is defined through the concept of electric potential difference, which also involves the unit of charge, the Coulomb (C).

Electric potential difference, or voltage, is defined as the amount of work done or energy transferred per unit electric charge to move the charge between two points. Mathematically, this can be expressed as:

\(V = \frac{W}{Q}\)

Where:

• \(V\) is the electric potential difference (measured in Volts, V)
• \(W\) is the work done or energy transferred (measured in Joules, J)
• \(Q\) is the electric charge (measured in Coulombs, C)

From this definition, we can see how the units are related. One Volt is defined as the potential difference between two points such that one Joule of work is done in moving one Coulomb of charge from one point to the other. Therefore, the relationship between the units is:

\(1 \text{ V} = \frac{1 \text{ J}}{1 \text{ C}}\)

Analyzing the Given Options

Let's examine each option based on this fundamental relationship:

• Option 1: \(\(1 J = \frac{1V}{1C}\)\)
• This option states \(1 \text{ J} = \frac{1 \text{ V}}{1 \text{ C}}\). If we rearrange our correct formula \(1 \text{ V} = \frac{1 \text{ J}}{1 \text{ C}}\), we get \(1 \text{ J} = 1 \text{ V} \times 1 \text{ C}\). So, this option is incorrect.
• Option 2: \(1J = 1V - 1C\)
• This option suggests subtracting a value in Volts from a value in Coulombs to get a value in Joules. This is dimensionally incorrect in physics. Units must be consistent in addition or subtraction.
• Option 3: \(1V = 1J \times 1C\)
• This option states \(1 \text{ V} = 1 \text{ J} \times 1 \text{ C}\). Based on our definition \(1 \text{ V} = \frac{1 \text{ J}}{1 \text{ C}}\), this means \(1 \text{ V} = 1 \text{ V} \times (1 \text{ C})^2\), which is incorrect.
• Option 4: \(\(1V=\frac{1J}{1C}\)\)
• This option states \(1 \text{ V} = \frac{1 \text{ J}}{1 \text{ C}}\). This directly matches the definition of one Volt as one Joule per one Coulomb.

Based on the analysis, Option 4 correctly represents the relationship between Volt, Joule, and Coulomb derived from the definition of electric potential difference.

Revision Table: Key Electrical Units

Additional Information: Connecting Electrical Concepts

The relationship \(V = \frac{W}{Q}\) is fundamental in understanding electrical circuits and phenomena. It links the energy involved in moving charges to the potential difference they move through. This concept is crucial for understanding power (Power \(P = \frac{W}{t}\)), where \(P = VI\) (since \(W = VQ\) and \(I = \frac{Q}{t}\)), and Ohm's law (\(V = IR\)), which relates voltage, current, and resistance.

The Joule is the standard SI unit for energy and work, used across many areas of physics, not just electricity. The Coulomb is the SI unit for electric charge, representing the charge carried by approximately \(6.24 \times 10^{18}\) electrons.