- AStatement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
- BStatement - 1 is True, Statement - 2 is True; Statement - 2 is NOT a correct explanation for Statement - 1
- CStatement - 1 is True, Statement - 2 is False
- DStatement - 1 is False, Statement - 2 is True
View written solutionFree
Correct answer: D
Analysis of Statement-2
- Statement-2: "Resistance of a metal increases with increase in temperature."
- This statement describes the behavior of electrical resistance in metallic conductors. For most metals, the relationship between resistance
Rand temperatureTis given by the formula: where is the resistance at temperatureT, is the resistance at a reference temperature, is the change in temperature, and is the temperature coefficient of resistance. - For metals, the temperature coefficient of resistance is positive. This means that as the temperature increases (), the resistance also increases.
- The physical reason for this is that an increase in temperature causes the ions in the metal lattice to vibrate with greater amplitude. This increases the frequency of collisions between the free electrons (charge carriers) and the lattice ions, which impedes the flow of electrons and thus increases the electrical resistance.
- Therefore, Statement-2 is True.
Analysis of Statement-1
-
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."
-
A Meter Bridge operates on the principle of a balanced Wheatstone bridge. Let the unknown resistance be
Xand the standard resistance from the resistance box beR. -
If the null point is found at a distance
lfrom the end whereXis connected, the balancing condition is: Assuming the meter bridge wire is uniform, the resistance is proportional to the length. So, (Equation 1) -
Now, the unknown resistance
Xis placed in an enclosure at a higher temperature. According to Statement-2 (which is true), the resistance ofXwill increase. Let the new resistance beX'. So,X' > X. -
The statement claims that the null point can be obtained at the same point
l. This means the ratiol / (100 - l)remains constant. -
To achieve this, the value of the standard resistance is changed to a new value, let's call it
R'. The new balancing condition will be: (Equation 2) -
Since the right-hand sides of Equation 1 and Equation 2 are the same, we can equate their left-hand sides:
-
We can solve for the new standard resistance
R': -
We established that heating the unknown resistance increases its value, so
X' > X. This implies that the ratio(X' / X) > 1. -
Therefore,
R' > R. This means that to maintain the null point at the same position, the standard resistanceRmust be increased. -
Statement-1 asserts that the standard resistance must be decreased. This is a contradiction to our derivation.
-
Therefore, Statement-1 is False.
Conclusion
- Statement-1 is False.
- Statement-2 is True.
This corresponds to option D.
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