Concept:Because a semiconductor diode has a non-linear characteristic curve, its resistance to small AC signals is defined as the reciprocal slope of the I-V curve at the operating point.
Formula:$$r_d = \frac{\Delta V_f}{\Delta I_f} = \left( \frac{d I_f}{d V_f} \right)^{-1} = \frac{\eta k T}{q I_f} = \frac{\eta V_T}{I_f}$$
Solution:- Dynamic resistance is the ratio of a small change in forward voltage (\( \Delta V_f \)) to the resulting change in forward current (\( \Delta I_f \)).
- In conducting silicon diodes, \( r_d \) is typically a few ohms (\( 1\text{–}25\ \Omega \)).
Why other options are incorrect:- Option B: \( V_f \times I_f \) represents power dissipation (in Watts), not electrical resistance.
- Option C: \( V_f / I_f \) defines static (DC) resistance, not dynamic (AC) resistance.
- Option D: \( \Delta I_f / \Delta V_f \) defines dynamic conductance (\( g_d \)), the reciprocal of resistance.
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