Concept:The dynamic (AC) resistance is calculated as the ratio of the change in forward voltage to the resulting change in forward current across a segment of the I-V curve.
Formula:$$r_d = \frac{\Delta V_f}{\Delta I_f}$$
Solution:- Calculate change in voltage: \( \Delta V_f = 0.74\text{ V} - 0.70\text{ V} = 0.04\text{ V} \).
- Calculate change in current: \( \Delta I_f = 30\text{ mA} - 10\text{ mA} = 20\text{ mA} = 0.02\text{ A} \).
- Calculate dynamic resistance:
- $$r_d = \frac{0.04\text{ V}}{0.02\text{ A}} = 2.0\text{ }\Omega$$
Why other options are incorrect:- Option A: \( 0.5\text{ }\Omega \) is the reciprocal (\( \frac{\Delta I}{\Delta V} = 0.5\text{ }\Omega^{-1} \)), which represents dynamic conductance.
- Option B: \( 4.0\text{ }\Omega \) results from using \( \Delta I = 10\text{ mA} \).
- Option D: \( 20.0\text{ }\Omega \) results from an error in converting milliamperes to amperes.
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