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: Understanding the Concept:
Electric potential difference between two points is defined as the work done per unit charge in moving a charge from one point to the other.
Step 2: Key Formula or Approach:
The formula relating potential difference (\( \Delta V \)), work done (W), and charge (q) is:
\[ \Delta V = V_B - V_A = \frac{W_{A \to B}}{q} \] where \( V_B - V_A \) is the potential difference between points B and A, and \( W_{A \to B} \) is the work done in moving the charge q from A to B.
Step 3: Detailed Explanation:
We are given:
- The work done, \( W = 12 \) J.
- The charge being moved, \( q = 3 \) C.
We need to find the potential difference, \( \Delta V \).
Using the formula:
\[ \Delta V = \frac{W}{q} \] Substitute the given values:
\[ \Delta V = \frac{12 \text{ J}}{3 \text{ C}} \] \[ \Delta V = 4 \text{ V} \] The unit Joules per Coulomb (J/C) is defined as a Volt (V).
Step 4: Final Answer:
The potential difference between A and B is 4 V. This corresponds to option (B).