IIT-JEE 2010 · Paper 1 · Physics Q73

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PhysicsSingle correct+3 / -1Question 73 of 84

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Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature $T_c(0)$ . An interesting property of superconductors is that their critical temperature becomes smaller than $T_c(0)$ if they are placed in a magnetic field, i.e., the critical temperature $T_c(B)$ is a function of the magnetic field strength B. The dependence of $T_c(B)$ on B is shown in the figure.

T_c(B) against B: starts at T_c(0) on the vertical axis and decreases, falling ever more steeply, to zero at a finite B.

In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields $B_1$ (solid line) and $B_2$ (dashed line). If $B_2$ is larger than $B_1$ , which of the following graphs shows the correct variation of R with T in these fields?

R against T: the dashed B₂ curve jumps from zero at a lower temperature than the solid B₁ curve; above their transitions both follow the same normal-state line.

R against T: both transitions at the same temperature; above it the dashed B₂ curve lies higher than the solid B₁ curve.

R against T: the solid B₁ curve jumps at a lower temperature than the dashed B₂ curve; above both they follow the same line.

R against T: both transitions at the same temperature; above it the dashed B₂ curve lies lower than the solid B₁ curve.

Answer and worked solution

Official answer: A

Effect of the field. $T_c(B)$ decreases with $B$ , so the larger field $B_2$ makes the resistance drop to zero at a lower temperature. Above the transition, in the normal state, the resistance follows the same curve in both fields.

That is graph (A): the dashed ( $B_2$ ) curve becomes superconducting at a lower $T$ than the solid ( $B_1$ ) curve.

(A)

Topics:Temperature dependence of resistance

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IIT-JEE 2010 · Paper 1, Physics question 73