Concept:Dynamic (AC) resistance is defined as the ratio of a change in forward voltage to the resulting change in forward current.
Formula:$$r_d = \frac{\Delta V_f}{\Delta I_f}$$
Solution:- Change in voltage: \( \Delta V_f = 0.75\text{ V} - 0.70\text{ V} = 0.05\text{ V} \).
- Change in current: \( \Delta I_f = 30\text{ mA} - 10\text{ mA} = 20\text{ mA} = 0.020\text{ A} \).
- Dynamic resistance: \( r_d = \frac{0.05\text{ V}}{0.020\text{ A}} = \frac{50\text{ mV}}{20\text{ mA}} = 2.5\ \Omega \).
Why other options are incorrect:- Option A: 5.0 Ω results from using \( \Delta I = 10\text{ mA} \) instead of 20 mA.
- Option C: 10.0 Ω results from using \( \Delta I = 5\text{ mA} \).
- Option D: 25.0 Ω is \( 0.75 / 0.030 \), which calculates static (DC) resistance instead of dynamic (AC) resistance.
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