Assertion: For measuring resistance of an ionic solution an AC source is used. Reason: Concentration of ionic

NCERT Exemplar · Q65

Q. Assertion: For measuring resistance of an ionic solution an AC source is used. Reason: Concentration of ionic solution will change if DC source is used.

(i) Both assertion and reason are true and the reason is the correct explanation of assertion.

(ii) Both assertion and reason are true and the reason is not the correct explanation of assertion.

(iii) Assertion is true but the reason is false.

(iv) Both assertion and reason are false.

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Concept understanding — Molar Conductivity

From Resistance to Conductance: Flipping the Idea

You already know resistance ( $R$ ) — it tells you how much a material opposes the flow of current. A high resistance means the wire fights the current; a low resistance means it lets current through easily.

Now flip that thought. Instead of asking "how much does it resist?", ask "how easily does it let current flow?" That's exactly what conductance measures.

Note

Conductance ( $G$ ) is the reciprocal of resistance:

$G = \frac{1}{R}$

Unit: siemens (S) — named after Werner von Siemens. 1 S = 1 A/V (ampere per volt).

If a wire has $R = 10\ \Omega$ , its conductance is $G = 0.1\ \text{S}$ . If $R = 0.5\ \Omega$ , $G = 2\ \text{S}$ — it conducts twice as well.

Ohm's Law in Conductance Form

You know $V = IR$ . Rearranging:

I = \frac{V}{R} = G V

So current = conductance × voltage. A high-conductance material draws a large current for the same voltage — it's a "good conductor."

Now, Conductivity: The Material's Intrinsic Property

Resistance depends on two things: the material itself (its "resistivity" $\rho$ ) and the geometry (length $L$ , cross-sectional area $A$ ):

R = \rho \frac{L}{A}

Conductance also depends on geometry. A thicker wire (larger $A$ ) or a shorter wire (smaller $L$ ) has higher conductance. To isolate the material's inherent ability to conduct, we define conductivity ( $\sigma$ ):

\sigma = \frac{1}{\rho}

Conductivity is the reciprocal of resistivity. It tells you how well the material itself conducts, independent of shape and size.

Unit: siemens per metre (S/m).
High $\sigma$ → good conductor (copper: $\approx 5.8 \times 10^7\ \text{S/m}$ ).
Low $\sigma$ → poor conductor / insulator (glass: $\approx 10^{-12}\ \text{S/m}$ ).

Watch out

Don't confuse conductance (property of a specific object, depends on geometry) with conductivity (property of the material, independent of geometry). A short thick copper wire has high conductance; a long thin copper wire has lower conductance — but both have the same conductivity.

The Big Picture in One Table

Quantity	Symbol	Definition	Depends on	Unit
Resistance	$R$	$V/I$	Material + geometry	$\Omega$
Resistivity	$\rho$	$R A / L$	Material only	$\Omega \cdot \text{m}$
Conductance	$G$	$1/R$	Material + geometry	S
Conductivity	$\sigma$	$1/\rho$	Material only	S/m

Intuitive Analogy

Think of a water pipe:

Resistance = how hard it is to push water through (narrow, long pipe).
Conductance = how easily water flows (wide, short pipe). …

Why this formula?

Conductance and Conductivity: Why the Formulas Hold

Let's build this from first principles — understanding the why before the what.

1. The Core Idea: How Easily Does Current Flow?

Think of a conductor (like a copper wire). When you apply a voltage across it, electrons drift through the material. Two questions arise:

How much current flows for a given voltage? → This is conductance ( $G$ ).
How well does the material itself allow current? → This is conductivity ( $\sigma$ ).

The key distinction: Conductance depends on the size and shape of the object. Conductivity is an intrinsic property of the material.

2. Ohm's Law in Terms of Conductance

You know Ohm's law:

V = IR

But we can rewrite it as:

I = \frac{V}{R}

Define conductance $G$ as the reciprocal of resistance:

G = \frac{1}{R}

So:

I = G V

Why this makes sense:

A larger $G$ means more current for the same voltage — the conductor "conducts" better.
$G$ has units of siemens (S) = $\text{A/V}$ .

3. From Resistance to Conductivity: The Geometry Factor

Resistance of a uniform conductor depends on:

Length $L$ (longer → more resistance)
Cross-sectional area $A$ (thicker → less resistance)
Material property $\rho$ (resistivity)

The formula:

R = \rho \frac{L}{A}

Now, conductivity $\sigma$ is the reciprocal of resistivity:

\sigma = \frac{1}{\rho}

So:

R = \frac{1}{\sigma} \cdot \frac{L}{A}

Why this form?

If you double the length, electrons have to travel twice as far, colliding more → resistance doubles.
If you double the area, there's twice as many "lanes" for electrons → resistance halves.

4. The Key Formula: Conductance in Terms of Conductivity

Since $G = 1/R$ , we get:

G = \sigma \frac{A}{L}

This is the central relationship. Let's see why it holds:

$\sigma$ tells you how well the material conducts (intrinsic).
$A/L$ tells you how the geometry amplifies or reduces that.

Intuition:

A fat, short wire ( $A$ large, $L$ small) has high conductance.
A thin, long wire ( $A$ small, $L$ large) has low conductance.
A material with high $\sigma$ (like copper) gives higher $G$ than one with low $\sigma$ (like iron), for the same shape.

5. Microscopic Derivation (Why $\sigma$ Exists)

At the microscopic level, conductivity arises from electron motion:

\sigma = n e \mu

Where:

$n$ = number of free electrons per unit volume
$e$ = electron charge …

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The assertion is true because AC prevents electrolysis; the reason is also true because DC causes electrolysis, changing concentration. The reason correctly explains why AC is used, so option (i) is correct.

This is a classic question from electrochemistry that tests your understanding of why we use AC instead of DC when measuring the resistance (or conductivity) of an ionic solution. Let's break it down.

The core idea: what happens when current flows through an ionic solution?

An ionic solution conducts electricity by the movement of ions. When a direct current (DC) passes through it, the positive ions (cations) move toward the negative electrode (cathode) and the negative ions (anions) move toward the positive electrode (anode). At the electrodes, these ions undergo chemical reactions — this is called electrolysis. For example, if you have a copper sulfate solution, copper metal deposits on the cathode and oxygen gas may form at the anode. This changes the composition and concentration of the solution near the electrodes, and over time the bulk concentration also changes.
Why does concentration change matter for resistance measurement?

The resistance (or conductivity) of an ionic solution depends directly on the concentration of ions. If the concentration changes during the measurement, the resistance you measure will not be the true resistance of the original solution — it will be drifting. That makes the measurement unreliable.
How does AC solve this problem?

An alternating current (AC) reverses direction many times per second (typically 50 Hz or 1000 Hz in a conductivity meter). So in one half-cycle, a given ion moves toward one electrode; in the next half-cycle, it moves back toward the other electrode. The net displacement of any ion over many cycles is nearly zero. No sustained electrolysis occurs — no net chemical reaction, no deposition, no gas evolution. The concentration of the solution remains constant throughout the measurement.
Connecting assertion and reason

The assertion says: "For measuring resistance of an ionic solution an AC source is used." This is true — every conductivity meter uses AC. …

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Here’s a breakdown of the common mistakes students make on this concept and how to avoid each.

Common Mistake 1: Thinking DC works fine for ionic solutions

What students do wrong:

Students assume that since DC is used for metallic conductors, it should also work for ionic solutions. They miss the key difference — ions are charged particles that move and react at electrodes.

How to avoid:

Remember: In an ionic solution, DC causes electrolysis. Positive ions move to the cathode, negative ions to the anode, and they get discharged. This changes the concentration of the solution near the electrodes.

Key rule: For resistance measurement of electrolytes, always use AC to prevent net migration and electrolysis.

Common Mistake 2: Confusing “change in concentration” with “change in resistance”

What students do wrong:

Some think the reason is false because they believe concentration doesn’t change — they confuse it with the fact that resistance changes with temperature or electrode distance.

How to avoid:

Understand the electrochemical effect:

With DC, ions are consumed at electrodes (e.g., $H^+$ and $OH^-$ form water, or metal plates out).
This reduces the number of charge carriers locally, changing the concentration and thus the resistance.
With AC, the direction reverses rapidly, so no net chemical change occurs — concentration stays constant.

Common Mistake 3: Misinterpreting the Assertion-Reason relationship

What students do wrong:

Students often pick option (ii) — “Both true but reason is not correct explanation” — because they think the reason is true but not directly linked. Actually, the reason is the correct explanation.

How to avoid:

Trace the logic:

Assertion: AC is used.
Reason: DC changes concentration.
Why AC? Because DC would change concentration → that would alter the resistance you’re trying to measure. So the reason directly explains why AC is necessary.
Correct answer: (i) Both true, reason is correct explanation.

Common Mistake 4: Forgetting that AC prevents polarization

What students do wrong: …

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Q.Assertion: For measuring resistance of an ionic solution an AC source is used.
Reason: Concentration of ionic solution will change if DC source is used.

Concept understanding — Molar Conductivity

From Resistance to Conductance: Flipping the Idea

Ohm's Law in Conductance Form

Now, Conductivity: The Material's Intrinsic Property

The Big Picture in One Table

Intuitive Analogy

Why this formula?

Conductance and Conductivity: Why the Formulas Hold

1. The Core Idea: How Easily Does Current Flow?

2. Ohm's Law in Terms of Conductance

3. From Resistance to Conductivity: The Geometry Factor

4. The Key Formula: Conductance in Terms of Conductivity

5. Microscopic Derivation (Why $\sigma$ Exists)

Method: Cause-Effect Analysis (Assertion-Reason Evaluation)

Steps

Common Mistake 1: Thinking DC works fine for ionic solutions

Common Mistake 2: Confusing “change in concentration” with “change in resistance”

Common Mistake 3: Misinterpreting the Assertion-Reason relationship

Common Mistake 4: Forgetting that AC prevents polarization

Q.Assertion: For measuring resistance of an ionic solution an AC source is used. Reason: Concentration of ionic solution will change if DC source is used.

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Q.Assertion: For measuring resistance of an ionic solution an AC source is used.
Reason: Concentration of ionic solution will change if DC source is used.

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