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Current Electricity question

2008 · Shift 1 · Q57
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Current Electricity question

2008 · Shift 1 · Q57

JEE AdvancedPhysicsCurrent ElectricityMCQ+3 / −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. and STATEMENT - 2 Resistance of a metal increases with increase in temperature.
  1. A
    Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1
  2. B
    Statement - 1 is True, Statement - 2 is True; Statement - 2 is NOT a correct explanation for Statement - 1
  3. C
    Statement - 1 is True, Statement - 2 is False
  4. D
    Statement - 1 is False, Statement - 2 is True
View written solutionFree

Correct answer: D

Analysis of Statement-2

  1. Statement-2: "Resistance of a metal increases with increase in temperature."
  2. This statement describes the behavior of electrical resistance in metallic conductors. For most metals, the relationship between resistance R and temperature T is given by the formula: RT=R0(1+αΔT)R_T = R_0 (1 + \alpha \Delta T)RT​=R0​(1+αΔT) where RTR_TRT​ is the resistance at temperature T, R0R_0R0​ is the resistance at a reference temperature, ΔT\Delta TΔT is the change in temperature, and α\alphaα is the temperature coefficient of resistance.
  3. For metals, the temperature coefficient of resistance α\alphaα is positive. This means that as the temperature increases (ΔT>0\Delta T > 0ΔT>0), the resistance RTR_TRT​ also increases.
  4. 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.
  5. Therefore, Statement-2 is True.

Analysis of Statement-1

  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."

  2. A Meter Bridge operates on the principle of a balanced Wheatstone bridge. Let the unknown resistance be X and the standard resistance from the resistance box be R.

  3. If the null point is found at a distance l from the end where X is connected, the balancing condition is: XR=resistance of length lresistance of length (100−l)\frac{X}{R} = \frac{\text{resistance of length } l}{\text{resistance of length } (100-l)}RX​=resistance of length (100−l)resistance of length l​ Assuming the meter bridge wire is uniform, the resistance is proportional to the length. So, XR=l100−l\frac{X}{R} = \frac{l}{100-l}RX​=100−ll​ (Equation 1)

  4. Now, the unknown resistance X is placed in an enclosure at a higher temperature. According to Statement-2 (which is true), the resistance of X will increase. Let the new resistance be X'. So, X' > X.

  5. The statement claims that the null point can be obtained at the same point l. This means the ratio l / (100 - l) remains constant.

  6. 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: X′R′=l100−l\frac{X'}{R'} = \frac{l}{100-l}R′X′​=100−ll​ (Equation 2)

  7. Since the right-hand sides of Equation 1 and Equation 2 are the same, we can equate their left-hand sides: XR=X′R′\frac{X}{R} = \frac{X'}{R'}RX​=R′X′​

  8. We can solve for the new standard resistance R': R′=R(X′X)R' = R \left( \frac{X'}{X} \right)R′=R(XX′​)

  9. We established that heating the unknown resistance increases its value, so X' > X. This implies that the ratio (X' / X) > 1.

  10. Therefore, R' > R. This means that to maintain the null point at the same position, the standard resistance R must be increased.

  11. Statement-1 asserts that the standard resistance must be decreased. This is a contradiction to our derivation.

  12. Therefore, Statement-1 is False.

Conclusion

  • Statement-1 is False.
  • Statement-2 is True.

This corresponds to option D.

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