Relation between Potential Difference and Work Done

The relation between potential difference and work done is very important in the study of electricity. Potential difference is the difference in electric potential between two points in an electric circuit. Work done is the energy transferred from one point to another due to the potential difference. The relation between potential difference and work done can be derived using the following steps:

Defining Potential Difference
Potential difference is defined as the work done per unit charge in moving a charge from one point to another in an electric circuit. Mathematically,

V = W / Q

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

Deriving the Formula for Work Done
The work done in moving a charge from one point to another in an electric circuit is given by the product of the charge, potential difference, and the distance traveled. Mathematically,

W = Q × V × d

where d is the distance traveled.

Substituting the value of W in the first equation, we get

V = W / Q = (Q × V × d) / Q = V × d

Therefore, the work done in an electric circuit is directly proportional to the potential difference and the distance traveled.

Interpreting the Formula
The formula derived above shows that the work done in an electric circuit is directly proportional to the potential difference. This means that increasing the potential difference will increase the work done. Similarly, decreasing the potential difference will decrease the work done.

The formula also shows that the work done is directly proportional to the distance traveled. This means that increasing the distance traveled will increase the work done. Similarly, decreasing the distance traveled will decrease the work done.

Conclusion
In conclusion, the relation between potential difference and work done is given by the formula V = W / Q. This formula shows that the work done is directly proportional to the potential difference and the distance traveled. Understanding this relation is crucial in the study of electricity and is essential in solving problems related to electric circuits.