Question

STATEMENT-1 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. and STATEMENT-2 Resistance of a metal increases with increase in temperature. (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True

Short answer

(A) is the correct answer because both statements are true and Statement-2 is the correct explanation for Statement-1.

Step-by-step solution

Understanding Statement-1

In a Meter Bridge experiment, the null point is found when the bridge is balanced, which means the ratio of the known resistance to the unknown resistance is equal to the ratio of the lengths on the bridge wire. If the unknown resistance is increased by heating, the balance can be restored by reducing the known resistance.

Analyzing Statement-2

Resistance of a metal increases with an increase in temperature due to the increase in collisions between electrons and the lattice structure of the metal as it vibrates more at higher temperatures. This statement is a general property of conductors and is theoretically and experimentally true.

Relating Statement-2 with Statement-1

Statement-2 provides the reason why the unknown resistance in the Meter Bridge experiment would increase when the temperature is raised. Thus, Statement-2 is a correct explanation for the observation in Statement-1, which is that the same null point can be obtained if the standard resistance is decreased to balance out the increase in the unknown resistance.

Choosing the Correct Option

Since both statements are true and Statement-2 is the correct explanation for Statement-1, the correct answer is option (A).

Key concepts

Electrical Resistance

Electrical resistance is a measure of the opposition that a circuit presents to the flow of electric current. It's symbolized by the letter 'R' and is measured in ohms (\rOmega). Think of it as similar to friction that slows down an object sliding across a surface. In the case of electricity, resistance slows down the flow of electrons.

Several factors affect resistance, including the material's nature, its length, cross-sectional area, and temperature. Conductors, such as copper or aluminum, have low resistance, allowing current to flow easily, while insulators, like rubber or glass, have high resistance, which restricts current flow. As an equation, resistance can be calculated using Ohm's Law, which states that resistance is the ratio of voltage (V) to current (I):
\[ R = \frac{V}{I} \].

This concept is crucial when conducting experiments such as in the Meter Bridge setup, where unknown resistances are determined through the manipulation of known resistances and balancing the flow of current.

Temperature Effect on Resistance

The resistance of a material is not fixed; instead, it can change with environmental conditions, particularly temperature. For most metals, resistance increases as temperature rises. This phenomenon occurs because higher temperatures cause atoms in the metallic lattice to vibrate more vigorously, which in turn makes it harder for electrons to flow through the material—similarly to how it gets harder to walk through a crowded room when everyone is moving erratically.

This temperature effect is described by the formula:
\[ R = R_0(1 + \alpha(T - T_0)) \],
where:\[ R_0 \] is the original resistance,\[ \alpha \] is the temperature coefficient for the material, \[ T \] is the current temperature, and \[ T_0 \] is the reference temperature.

In the context of a Meter Bridge experiment, if one of the resistances being measured is subject to a temperature increase, this would result in changes to the balance point of the bridge—which needs to be considered in the experimental design and analysis of results.

Balancing a Wheatstone Bridge

A Wheatstone Bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. The primary equation governing a Wheatstone Bridge is based on the ratios of four resistances:
\[ \frac{R1}{R2} = \frac{R3}{Rx} \],
where \(R1\) and \(R2\) are known resistances, \(R3\) is an adjustable resistance, and \(Rx\) is the unknown resistance. The bridge is considered 'balanced' when the voltage across the bridge's middle is zero, and no current flows through the meter, thereby indicating that the ratio of resistances in one leg is equal to the ratio in the other leg.

A Meter Bridge operates on this principle using a sliding contact along a uniform resistance wire. In an experiment, if the bridge is balanced (handled by adjusting \(R3\) until the null point is achieved), one can accurately determine the value of the unknown resistance \(Rx\). The beauty of this setup is its simplicity and accuracy for resistance measurement, which is why it remains a staple in physics laboratories.