Concept:Dynamic resistance is the reciprocal slope of the diode's exponential forward I-V characteristic: \( r_d = (dI_F / dV_F)^{-1} \).
Formula:$$I_F = I_0 e^{\frac{V_F}{\eta V_T}} \implies \frac{d I_F}{d V_F} = \frac{I_F}{\eta V_T} \implies r_d = \frac{d V_F}{d I_F} = \frac{\eta V_T}{I_F}$$
Solution:- Differentiating the Shockley diode equation with respect to forward voltage yields \( r_d = \frac{\eta V_T}{I_F} \).
- At room temperature, \( V_T = \frac{k T}{q} \approx 26\text{ mV} \), so dynamic resistance decreases inversely with forward current \( I_F \).
Why other options are incorrect:- Option B: \( I_F / (\eta V_T) \) is the dynamic conductance \( g_d \), the reciprocal of resistance.
- Option C: Multiplying voltage by current does not give resistance.
- Option D: \( V_F / I_F^2 \) is dimensionally incorrect.
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