Which of the following represents the electric potential difference between two points? 

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  1. Work done / charge
  2. Electric charge / time
  3. Charge × work done
  4. Work done / time

Answer (Detailed Solution Below)

Option 1 : Work done / charge
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Detailed Solution

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Explanation:

Electric Potential Difference

Definition: The electric potential difference between two points in an electric field is defined as the work done to move a unit positive charge from one point to another. It is a measure of the potential energy per unit charge at a specific location in the field.

Formula: The electric potential difference (V) between two points is given by:

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

where V is the electric potential difference, W is the work done, and Q is the charge.

Explanation:

When a charge moves in an electric field, work is done by or against the electric field. The amount of work done per unit charge is called the electric potential difference. This concept is analogous to gravitational potential difference, where work is done to move a mass in a gravitational field.

Units: The SI unit of electric potential difference is the volt (V). One volt is equivalent to one joule per coulomb (1 V = 1 J/C).

Correct Option Analysis:

The correct option is:

Option 1: Work done / charge

This option correctly describes the electric potential difference. The work done to move a charge from one point to another divided by the amount of charge gives the electric potential difference. Mathematically, this is represented as:

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

where V is the electric potential difference, W is the work done, and Q is the charge.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Electric charge / time

This option describes the concept of electric current, not electric potential difference. Electric current (I) is defined as the rate of flow of electric charge (Q) through a conductor per unit time (t). Mathematically, it is expressed as:

\( I = \frac{Q}{t} \)

The unit of electric current is the ampere (A).

Option 3: Charge × work done

This option does not represent any standard electrical quantity. Multiplying charge (Q) by work done (W) does not yield electric potential difference or any other commonly used electrical parameter.

Option 4: Work done / time

This option describes the concept of power, not electric potential difference. Power (P) is defined as the rate at which work (W) is done or energy is transferred per unit time (t). Mathematically, it is expressed as:

\( P = \frac{W}{t} \)

The unit of power is the watt (W).

Conclusion:

Understanding the distinction between different electrical concepts is crucial. The electric potential difference specifically refers to the work done to move a unit charge between two points in an electric field, and is accurately represented by the formula \( V = \frac{W}{Q} \). Other options describe different electrical quantities such as electric current and power, but do not pertain to electric potential difference.

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