Concept:On the exponential forward I-V characteristic, the dynamic resistance (reciprocal of the tangent slope) is smaller than the static resistance (reciprocal of the secant slope from the origin).
Formula:$$R_D = \frac{V_F}{I_F} \quad (\text{Secant slope}^{-1}), \quad r_d = \frac{dV_F}{dI_F} \quad (\text{Tangent slope}^{-1}) \implies R_D > r_d$$
Solution:- In the region above the knee voltage, current increases exponentially with voltage.
- The tangent to the curve is steeper than the secant line drawn from the origin to the operating point.
- Because dynamic resistance is the reciprocal of the tangent slope and static resistance is the reciprocal of the secant slope, \( R_D > r_d \).
Why other options are incorrect:- Option B: \( R_D = r_d \) occurs only in linear, ohmic resistors.
- Option C: Because the curve bends upward, the tangent is always steeper than the secant, so \( r_d \) cannot exceed \( R_D \).
- Option D: Both resistances have finite positive values in forward conduction.
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