Assertion: In a meter bridge experiment, null point for an unknown resistance is measured. Now, the

Q: Why does the resistance of a metal increase with temperature?

As temperature increases, the atoms in the metal vibrate more vigorously. This increases the frequency of collisions between the flowing free electrons and the atoms, thereby increasing the resistance.

Q: What happens if we don't change $R$ when $X$ increases?

If $R$ is kept constant while $X$ increases, the ratio $R/X$ decreases. To balance the bridge, the ratio $l_1/l_2$ must also decrease, which means the null point will shift towards the left (smaller $l_1$).

Q: Can we use a semiconductor instead of a metal for $X$?

Yes, but semiconductors behave differently! Their resistance *decreases* with an increase in temperature. If $X$ were a semiconductor, we would actually need to decrease $R$ to keep the null point unchanged.

Q: Why is the meter bridge wire exactly 100 cm long?

It's a matter of convenience for calculations and standard laboratory design. A 1-meter wire provides a good balance of measurable length and manageable resistance, making it easy to read $l_1$ and calculate $l_2 = 100 - l_1$.

Q: Is the galvanometer reading affected by temperature?

While the galvanometer coil's resistance might change slightly with temperature, it doesn't affect the null point. At the null point, zero current flows through the galvanometer, so its resistance doesn't enter the balance equation!

Question

**Assertion:** In a meter bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.

**Reason:** Resistance of a metal increases with increase in temperature.

Options:

(A) If Assertion is true, Reason is true; Reason is the correct explanation for Assertion

(B) If Assertion is true, Reason is true; Reason is not a correct explanation for Assertion

(C) If Assertion is true; Reason is false

(D) If Assertion is false; Reason is true

Sigma Percentile · Accepted Answer

Have you ever wondered how we can measure resistance with such incredible precision? The meter bridge is a beautiful application of the Wheatstone bridge principle, allowing us to find unknown resistances by simply sliding a jockey along a wire.

But what happens when we introduce a twist—like changing the temperature? Let's dive into this fascinating problem and unravel the physics step by step!

### Analyzing the Setup

Imagine you are standing in front of a meter bridge.

In the left gap, we have a standard, known resistance $R$. In the right gap, we have our mysterious unknown resistance $X$.

When we slide the jockey and find the null point, the galvanometer shows zero deflection. This means the bridge is perfectly balanced! The wire is divided into two segments: $l_1$ and $l_2$.

### The Master Equation

Because the bridge is balanced, the ratio of the resistances in the gaps is exactly equal to the ratio of the balancing lengths.

We can write this elegantly as:
$$ \frac{R}{X} = \frac{l_1}{l_2} $$

This is our master equation. It dictates the entire behavior of the meter bridge.

### The Temperature Twist

Now, the problem throws a curveball. We take the unknown resistance $X$ and place it inside a hot enclosure.

What does heat do to a metal?

As the Reason statement correctly points out, the resistance of a metal increases with an increase in temperature. The thermal agitation of atoms makes it harder for electrons to flow.

Therefore, the value of our unknown resistance $X$ goes up!

### Maintaining the Balance

The Assertion states that we want to obtain the null point at the **exact same position** as before.

If the null point doesn't move, the lengths $l_1$ and $l_2$ remain completely unchanged.

This means the ratio on the right side of our master equation, $\frac{l_1}{l_2}$, is a constant.

If the right side is constant, the left side must also be constant:
$$ \frac{R}{X} = 	ext{constant} $$

### The Final Verdict

Let's look closely at this ratio. We know that the denominator, $X$, has increased due to the heat.

For the entire fraction $\frac{R}{X}$ to remain constant, the numerator $R$ must also increase proportionally!

We need a **larger** standard resistance to maintain the balance at the same point.

However, the Assertion claims that we should **decrease** the value of the standard resistance. This is a direct contradiction to our physical deduction.

Therefore, the Assertion is completely false, while the Reason is a true statement of physics.

The correct choice is option (d). Physics is all about following the logic, and here, the logic leads us straight to the answer!

Select Answer:

Visualized Solution

$Meter Bridge Setup$

$Balanced Condition$

$Effect of Temperature$

$Maintaining the Null Point$

$Adjusting Standard Resistance$

$Conclusion$

The Sigma Insight: Electrical Instruments

Analyzing the Setup

The Master Equation

The Temperature Twist

Maintaining the Balance

The Final Verdict

Similar Questions

$R_{1}, R_{2}, R_{3}$ are different values of $R$ . Further, $A, B$ and $C$ are the null points obtained corresponding to $R_{1}, R_{2}$ and $R_{3}$ respectively. For which resistor, the value of $X$ will be the most accurate and why?

During an experiment with a meter bridge, the galvanometer shows a null point when the jockey is pressed at $40.0 cm$ using a standard resistance of $90 Ω$ , as shown in the scale used in the meter bridge is $1 mm$ . The unknown resistance is

In the shown arrangement of the experiment of the meter bridge if $A C$ corresponding to null deflection of galvanometer is $x$ , what would be its value if the radius of the wire $A B$ is doubled ?

Shown in the figure adjacent is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resistor $R$ is

Select Answer:

Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Meter Bridge Setup

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Balanced Condition

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Effect of Temperature

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Maintaining the Null Point

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Adjusting Standard Resistance

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Conclusion