Semiconductors: PYQ Walkthrough (4)

Question

(NEET 2022 style) In a p-n junction diode, the current flowing under forward bias is $10$ mA at room temperature. Find the dynamic resistance of the diode if the voltage is changed by $20$ mV and the current changes to $20$ mA.

Solution — Step by Step

Final Answer: $r_d = 2$ Ω.

Why This Works

A diode is a non-linear device — its V–I curve bends, so a single resistance value can’t describe it across all operating conditions. Dynamic resistance captures the local slope where the device is operating, which is what matters for small-signal AC analysis.

In forward bias near the knee voltage, $r_d$ is typically a few ohms. In reverse bias, it shoots up to megaohms because the curve is nearly flat (negligible current).

Alternative Method

The Shockley diode equation gives $r_d = nkT/qI \approx 25/I_{\text{mA}}$ Ω at room temperature with $n = 1$. For $I = 15$ mA (the average of $10$ and $20$ mA), $r_d \approx 25/15 \approx 1.7$ Ω. Close to our $2$ Ω — the discrepancy is because the question uses a finite difference, not a true derivative.