Inductor voltage law: For a coil with L = 8 µH, if di/dt = 20 mA/µs, what is the induced voltage across the coil (v = L * di/dt)?

Introduction / Context:The defining inductor relation v = L * di/dt directly links voltage to how quickly current changes. Mastering unit conversions (µH, mA/µs) is critical for translating lab measurements into correct voltage estimates, especially in switching converters and transient analysis.

Given Data / Assumptions:

• L = 8 µH = 8 × 10^-6 H.
• di/dt = 20 mA/µs = 20 × 10^-3 A per 10^-6 s = 2.0 × 10^4 A/s.
• Ideal inductor; polarity per Lenz's law is not required for magnitude.

Concept / Approach:Apply the formula v = L * di/dt using consistent SI units. Convert microhenry to henry and milliampere-per-microsecond to ampere-per-second before multiplying to avoid powers-of-ten errors.

Step-by-Step Solution:

Verification / Alternative check:Scale check: 10 µH * 10 mA/µs → 0.1 V. Our L and di/dt are close, giving ≈0.16 V, which is consistent by proportionality.

Why Other Options Are Wrong:

• 16 mV or 1.6 mV or 2.5 mV: These miss factors of 10^1–10^2 due to unit-conversion mistakes.

Common Pitfalls:

• Treating mA/µs as mA/s or forgetting to convert µH to H.

Final Answer:160 mV