Question

Assertion (A) : The work done, in taking a unit charge around a closed loop of an electric circuit involving cells and resistors in the loop, is zero. Reason (R) : The potential at a point depends on the location of the point in the loop. After completing one round, the charge comes back to the point of start.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

Always remember Kirchhoff's Loop Rule: \[ \sum \Delta V = 0 \] around any closed circuit loop. Therefore, net work done per unit charge in one complete round is zero.

Answer 1

The Correct Option is C

Concept: According to Kirchhoff's loop rule, the algebraic sum of potential differences around a closed loop is zero. \[ \sum \Delta V = 0 \] This implies that the net work done per unit charge in moving around a complete closed loop is zero.

Step 1: Examine the Assertion. The assertion states that the work done in taking a unit charge around a complete closed loop containing cells and resistors is zero. According to Kirchhoff's voltage law, \[ \sum \Delta V = 0 \] for a complete closed loop. Hence, the net work done per unit charge after completing one round of the circuit is zero. Therefore, the Assertion is true.

Step 2: Examine the Reason. The reason states that the potential at a point depends on the location of the point in the loop and after completing one round the charge comes back to the starting point. The second statement that the charge returns to the starting point is correct. However, the statement \[ \text{``The potential at a point depends on the location of the point in the loop''} \] is not the reason for the net work done becoming zero. The actual reason is that potential is a state function and the algebraic sum of all potential changes around a closed loop is zero. Thus the given Reason is considered false.

Step 3: Final conclusion. Assertion is true but Reason is false. \[ \boxed{\text{(C)}} \]