Superconductivity basics for electrical engineering When a material is in the superconducting state (below its critical temperature, magnetic field, and current limits), what is the electrical resistance of the superconductor under steady direct current conditions?

Introduction / Context:
Superconductivity is a quantum state of certain materials in which they lose all electrical resistance and expel magnetic fields (Meissner effect) below specific critical limits. Understanding the correct value of resistance in this state is fundamental for power applications, magnetic resonance, cryogenic electronics, and high-field magnets.

Given Data / Assumptions:

• The material is already in the superconducting phase (temperature below Tc).
• Applied magnetic field and transport current are below their respective critical values.
• We are considering steady direct current (DC) conduction, not alternating current losses due to flux motion.

Concept / Approach:

In a superconductor carrying DC below its critical limits, the electrical resistivity is exactly zero. This is not merely a very small value; it is identically zero within the DC model. Persistent currents can flow indefinitely without a drop in terminal voltage because no Joule heating occurs. This is distinct from ordinary conductors where resistivity increases with temperature due to phonon scattering.

Step-by-Step Solution:

Verification / Alternative check:

Persistent currents in superconducting rings have been observed to persist for years without measurable decay, which is only possible if resistance is zero. AC conditions can introduce losses due to flux motion in type-II superconductors, but this does not contradict the DC zero-resistance property.

Why Other Options Are Wrong:

“Low”, “very low”, or “very very low” imply a finite resistance and hence Joule heating; that contradicts the defining feature of superconductivity. “Negligible but not zero” is also incorrect because zero is exact in the DC superconducting state.

Common Pitfalls:

Confusing DC zero resistance with AC losses; mixing up cryogenic high-purity metals (which have low but non-zero resistance) with the superconducting state (exactly zero DC resistance).

Final Answer:

zero