Empirical conduction law for a thyristor For a thyristor in forward conduction, the empirical relation i = k * v^a is sometimes used around the operating point. The approximate value of the exponent a is:

Introduction / Context:
While a piecewise linear model (on-state drop plus dynamic resistance) is common for SCRs, some analyses use an empirical power law i = k * v^a in the conduction region to capture the nonlinearity of the PNPN structure near a given operating point.

Given Data / Assumptions:

• Forward-conducting SCR after latching.
• Voltage v is the incremental on-state voltage above the knee.
• k is an empirical constant depending on device and temperature.

Concept / Approach:
In practice, the exponent a is near 2 in many thyristor conduction approximations, reflecting a moderately nonlinear current increase with voltage around the knee region. This offers a convenient analytical fit when precise device equations are not required.

Step-by-Step Solution:
Recognize that a < 1 would imply very weak nonlinearity (not typical).Very large a (e.g., 20) would indicate an extremely sharp rise, beyond practical ranges for averaged analysis.Empirical studies and texts frequently use a ≈ 2.

Verification / Alternative check:
Comparisons of i–v curves fitted around nominal operating currents show quadratic-like behavior in certain regions, supporting a ≈ 2 as a rough guide.

Why Other Options Are Wrong:

• 0.5 or 1/3: too shallow a slope for an SCR in conduction.
• 5 or 20: unrealistically steep for typical power ranges (would be closer to a switching step than a conduction curve).

Common Pitfalls:

• Treating the power law as universal; it is only a local fit around operating points and not a fundamental device law.

Final Answer:
about 2