The Question is from NEET guide , and it was created by the author ABDUL JILANI BASHA

Question

Which of the following factors does NOT affect the balancing length of a potentiometer?

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
	**Primary Concept**: Potentiometer Working Principle
	**Related Topics**: Kirchhoff's Laws, Ohm's Law, EMF, Potential Difference
	**Prerequisites**: Understanding of electric circuits and potential difference.
## SOLUTION PATHWAY
**Given Information**:
	We are looking for the factor that *doesn't* influence the balancing length of a potentiometer.
**Method & Steps**:
	1. **Recall the principle of a potentiometer:** A potentiometer measures an unknown emf by comparing it with a known emf.  At the balance point, the potential difference across a portion of the potentiometer wire (the balancing length) equals the unknown emf.
		Reasoning:  The balance length is determined when the galvanometer shows zero deflection, indicating no current flow through the test cell.  This happens when the potential difference across the balancing length is equal to the emf of the test cell.
		Formula/Rule:  $E_x = (\frac{E}{L})l$, where $E_x$ is the unknown emf, $E$ is the potential difference across the potentiometer wire, $L$ is the total length of the wire, and $l$ is the balancing length.
	2. **Analyze the formula:** The balancing length ($l$) is directly proportional to the unknown emf ($E_x$) and the total potential difference across the potentiometer wire ($E$), and inversely proportional to the total length ($L$) of the wire.  The specific resistance ($ho$) of the wire affects the total resistance, and thus the potential difference across the wire for a given current.  The cross-sectional area ($A$) also affects the resistance ($R = \frac{ho L}{A}$), but its effect is compensated by the current change, keeping the potential difference across the whole wire constant.
		Working: $E = IR = I(\frac{ho L}{A})$, while $I = \frac{V}{R_{total}}$.  If $R_{total}$ incorporates a large fixed resistor in series with the potentiometer wire, changing $A$ will negligibly affect $I$ and hence $E$, thus having no effect on $l$.
		Key Point: The potential difference across the potentiometer wire is what matters, not the individual factors that contribute to it (like specific resistance and cross-sectional area), as long as the driving source maintains a constant potential difference across the potentiometer wire.
	3. **Identify the independent factor:**  The cross-sectional area affects the resistance of the wire, but assuming a constant potential difference across the potentiometer wire, changes in cross-sectional area will be compensated by corresponding changes in current, leaving the balancing length unaffected.
		Result: The balancing length is independent of the cross-sectional area of the potentiometer wire.
		Verification: This aligns with the principle that the potentiometer compares potential differences, and the area of the wire doesn't directly influence the potential difference across the balancing length.
## OPTION ANALYSIS
[A] :x: Potential difference across the potentiometer wire ($E$): Affects the balancing length directly.  A higher potential difference across the potentiometer wire leads to a larger balancing length for the same emf.
[B] :x: emf of the test cell/battery ($E_x$):  Affects the balancing length directly.  A larger emf requires a longer balancing length.
[C] :x: Specific resistance of the potentiometer wire ($ho$): Affects the balancing length indirectly by affecting the potential difference across the wire. A higher specific resistance leads to a higher resistance and thus can influence the balancing length for a given current and potential difference across the wire.
[D] ✓: Cross-sectional area of the potentiometer wire ($A$): Does NOT directly affect the balancing length.  Although it affects the resistance of the wire, this effect is generally compensated by the current change, assuming a constant potential difference is maintained across the potentiometer wire.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing resistance with potential difference:  Remember the potentiometer balances potential differences, not resistances directly.
		2. Neglecting the constant potential difference assumption:  The independence of cross-sectional area holds true under the assumption of a constant potential difference across the potentiometer wire.
	**Quick Tips**:
		1. Focus on the potential difference:  The balancing length is directly proportional to the potential difference across the balancing length, which is equal to the unknown emf.
		2. Visualize the circuit:  Drawing the potentiometer circuit and labeling the potentials can help understand the factors influencing the balancing length.

ABDUL JILANI BASHA · Answer

Potential difference across the potentiometer wire

ABDUL JILANI BASHA · Answer

emf of the test cell/battery

ABDUL JILANI BASHA · Answer

Specific resistance of the potentiometer wire

ABDUL JILANI BASHA · Answer

The correct Option is "Cross-sectional area of the potentiometer wire"

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