For the forward biased diode characteristics shown in the figure, the dynamic resistance at I D = 3 mA will be __________ Ω.

Solution

Physics sir · 4 steps

Dynamic resistance is the slope of V against I near 3 mA, not V divided by I at one point.

1. What to find. Dynamic resistance is r_d = (Δ V)/(Δ I), a small change in voltage divided by the small change in current it causes. It is the inverse of the slope of the I–V curve at that point.
2. Read the graph. Near 3 mA the curve is a straight line. The dotted lines mark I_D = 3 mA at V_D = 0.70 V and I_D = 5 mA at V_D = 0.75 V.

   r_d = (Δ V)/(Δ I) = (0.75 - 0.70)/((5 - 3) × 10⁻³) = 0.05/(2 × 10⁻³) Ω

3. Check. The 1 mA point at 0.65 V lies on the same line: (0.70 - 0.65)/((3 - 1) × 10⁻³) = 25 Ω as well.
4. So. The dynamic resistance at I_D = 3 mA is 25 Ω.

The common slip: 233. Dividing V by I at a single point, 0.70/(3 × 10⁻³), gives the static resistance, about 233 Ω. The dynamic resistance needs changes in V and I.

The idea to keep. For a diode, dynamic resistance means Δ V/Δ I taken along the curve around the operating point. Convert mA to A before you divide.

Answer from the NTA final answer key. Solution by PrepWiser.