Question

If the work done in moving a charge of \( 3\,C \) from A to B is \( 12\,J \), then the potential difference between A and B is

• A. \( 5\,V \)
• B. \( 4\,V \)
• C. \( 36\,V \)
• D. \( 26\,V \)
• E. \( 10\,V \)

Hint:

Always remember: \[ V = \frac{W}{q} \] Work per unit charge gives potential difference.

Answer 1

The Correct Option is B

Step 1: Recall the definition of potential difference.
Potential difference is defined as work done per unit charge: \[ V = \frac{W}{q} \]

Step 2: Identify the given values.
Work done: \[ W = 12\,J \] Charge: \[ q = 3\,C \]

Step 3: Substitute into the formula.
\[ V = \frac{12}{3} \]

Step 4: Perform the calculation.
\[ V = 4\,V \]

Step 5: Interpret physically.
This means 4 joules of work is required to move 1 coulomb of charge between points A and B.

Step 6: Check units consistency.
\[ \text{Volt} = \frac{\text{Joule}}{\text{Coulomb}} \] So units are correct.

Step 7: Final conclusion.
Hence, the potential difference is: \[ \boxed{4\,V} \] Therefore, the correct option is \[ \boxed{(2)\ 4\,V} \]