Concept:When forward-biased beyond the knee voltage (\( V_k \approx 0.7\text{ V} \)), the diode's I-V curve becomes very steep, meaning small changes in voltage produce large changes in current (low dynamic resistance).
Formula:$$r_f = \frac{\Delta V_f}{\Delta I_f} = \frac{\eta V_T}{I_f} \approx \frac{26\text{ mV}}{I_f\text{ (mA)}} \quad (\text{at room temperature})$$
Solution:- For a typical forward current of \( I_f = 10\text{ mA} \), the dynamic resistance is \( r_f \approx \frac{26\text{ mV}}{10\text{ mA}} = 2.6\ \Omega \).
- Including semiconductor bulk and contact resistance, practical forward dynamic resistance ranges from \( 1\text{ to } 25\ \Omega \).
Why other options are incorrect:- Option A: Megaohms corresponds to the reverse-biased state.
- Option B: Kiloohms is typical for reverse bias near the origin or for low-current sub-threshold operation.
- Option D: Real semiconductor diodes always have non-zero bulk and contact resistance.
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