Resistance Variation of Superconductor in Magnetic Fields

Based on the provided passage and principles of superconductivity:

1. Dependence of Critical Temperature on Magnetic Field:
   The critical temperature $T_c(B)$ of a superconductor decreases as the applied magnetic field strength $B$ increases.
   Mathematically, if $B_2 > B_1$, then:
   $T_c(B_2) < T_c(B_1)$

2. Resistance as a Function of Temperature:
   A material behaves as a superconductor (having zero electrical resistance, $R = 0$) when its temperature $T$ is strictly less than its critical temperature $T_c(B)$ for a given magnetic field $B$:

   • For magnetic field $B_1$: $R = 0$ for $T \le T_c(B_1)$, and $R > 0$ for $T > T_c(B_1)$.
   • For magnetic field $B_2$: $R = 0$ for $T \le T_c(B_2)$, and $R > 0$ for $T > T_c(B_2)$.

3. Comparison of Transition Points:
   Since $B_2 > B_1$, the critical temperature $T_c(B_2)$ for field $B_2$ (dashed line) must lie to the left of $T_c(B_1)$ for field $B_1$ (solid line) on the temperature ($T$) axis.

4. Evaluating the Options:

   • Graph A: Shows the abrupt drop in resistance for the dashed line ($B_2$) occurring at a lower temperature than that for the solid line ($B_1$), i.e., $T_c(B_2) < T_c(B_1)$.
   • Graph C: Incorrectly shows $T_c(B_1) < T_c(B_2)$.
   • Graphs B and D: Incorrectly represent the normal state resistance and transition behavior.

Therefore, the correct variation of $R$ with $T$ is given by option A.