The Question is from neet-physics current-electricity , and it was created by the author ABDUL JILANI BASHA

Question

Two potentiometers, P1 and P2, have identical wires and driver cells. However, P1 uses a rheostat with a higher resistance range than P2.  Which potentiometer will offer greater sensitivity in balancing a given cell?

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Sensitivity of a Potentiometer
	**Related Topics**: Potential difference, Resistance, Current
	**Prerequisites**: Understanding of potentiometer working principle
## SOLUTION PATHWAY
**Given Information**:
	* Two potentiometers, P1 and P2, with identical wires and driver cells.
	* P1 has a higher resistance rheostat than P2.
**Method & Steps**:
	1. **Sensitivity Definition**: The sensitivity of a potentiometer is its ability to measure small potential differences.  A more sensitive potentiometer can detect smaller changes in potential.
		Reasoning: Higher sensitivity means a smaller potential difference causes a larger deflection in the balancing point.
	2. **Potential Gradient**: The potential gradient ($\frac{dV}{dl}$) along the potentiometer wire is crucial for sensitivity. A smaller potential gradient means higher sensitivity.
		Working:  Potential gradient is directly proportional to the current flowing through the potentiometer wire and inversely proportional to the length of the wire. Since the wires are identical, the length is the same.  With identical driver cells, the current is determined by the total resistance in the circuit (driver cell internal resistance + rheostat resistance + wire resistance). 
		Key Point: A larger rheostat resistance leads to a smaller current.
	3. **Relating Rheostat to Sensitivity**: A higher resistance rheostat (P1) will result in a smaller current, leading to a smaller potential gradient and thus higher sensitivity.
		Result: P1 has higher sensitivity than P2.
		Verification:  The smaller the potential gradient, the larger the change in balancing length for a given change in potential difference being measured, hence higher sensitivity.
 ## OPTION ANALYSIS
[A] ✓: P1 has a higher resistance rheostat, leading to a smaller potential gradient and therefore higher sensitivity.
[B] :x: P2 has a lower resistance rheostat, resulting in a larger potential gradient and lower sensitivity.
[C] :x: The sensitivity is directly affected by the rheostat resistance.
[D] :x: The sensitivity of the potentiometer is determined by its potential gradient, which is independent of the cell being balanced. While the null point will depend on the cell being balanced, the sensitivity won't.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing balancing length with sensitivity: The balancing length changes with the emf being measured, but sensitivity is about how much the balancing length changes for a *given* change in emf.
		2. Ignoring the effect of the rheostat: The rheostat plays a crucial role in controlling the current and thus the potential gradient.
	**Quick Tips**:
		1. Remember: Higher rheostat resistance → Lower current → Smaller potential gradient → Higher sensitivity.
		2. Visualize: Imagine a very sensitive potentiometer – a small change in the emf being measured should cause a large shift in the balancing point.

ABDUL JILANI BASHA · Answer

The correct Option is "P1"

ABDUL JILANI BASHA · Answer

P2

ABDUL JILANI BASHA · Answer

Both P1 and P2 will have the same sensitivity

ABDUL JILANI BASHA · Answer

Sensitivity depends on the cell being balanced, not the potentiometer

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