---
title: "Resistance of a germanium diode"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:germanium-diode-resistance"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/germanium-diode-resistance
site: BCT Engineering
---

# Resistance of a germanium diode

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2076 Chaitra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/germanium-diode-resistance
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

Find the resistance of p-n junction Germanium diode if temperature is 27°C and I₀ = 1μA for an applied forward bias of 0.2 Volt.

## Short answer

Using Shockley equation with V_T=0.02585 V, forward current = 1 µA × (e^(0.2/0.02585)−1) ≈ 2.29 mA. Static resistance R_DC = 0.2 V / 2.29 mA ≈ 87.3 Ω; dynamic resistance r_d ≈ 0.02585 V / 2.29 mA ≈ 11.3 Ω.

## Answer

The diode current is given by the Shockley diode equation

$$
I = I_0\left(e^{V/\eta V_T}-1\right)
$$

with $\eta = 1$ for germanium and $V_T = kT/e$.

**Given:** $T = 27^\circ\text{C} = 300$ K, $I_0 = 1\ \mu\text{A}$, $V = 0.2$ V.

$$
V_T = \frac{kT}{e} = \frac{1.38\times10^{-23}\times300}{1.6\times10^{-19}} = 0.02585\ \text{V}
$$

#### Forward current

$$
\begin{aligned}
\frac{V}{V_T} &= \frac{0.2}{0.02585} = 7.737\\
e^{7.737} &= 2291.5\\
I &= 10^{-6}(2291.5-1) = 2.29\times10^{-3}\ \text{A} = 2.29\ \text{mA}
\end{aligned}
$$

#### Static (DC) resistance

$$
R_{DC} = \frac{V}{I} = \frac{0.2}{2.29\times10^{-3}} = 87.3\ \Omega
$$

#### Dynamic (AC) resistance

$$
\begin{aligned}
r_d &= \frac{dV}{dI} = \frac{\eta V_T}{I+I_0}\\
&= \frac{0.02585}{2.29\times10^{-3}+10^{-6}} = 11.3\ \Omega
\end{aligned}
$$

**Answer: forward current ≈ 2.29 mA; static resistance ≈ 87.3 Ω; dynamic resistance ≈ 11.3 Ω.**

The static value is the ratio V/I at the operating point; the dynamic value is the slope resistance seen by small signals.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which equation gives the forward current?
   A. I = I0 (exp(V/eta V_T) - 1) with eta = 1 for Ge
   B. I = I0 exp(-V/V_T)
   C. I = V/I0
   D. I = I0 (V_T/V)
   Answer: A. Shockley diode equation. (Key point: Equation)

2. What is V_T at 27 degrees C?
   A. 0.0259 mV
   B. kT/e = 0.02585 V
   C. 0.2585 V
   D. 2.585 V
   Answer: B. k = 1.38e-23, T = 300 K, e = 1.6e-19. (Key point: Thermal voltage)

3. What is the DC resistance for 0.2 V?
   A. V/I = 0.2/2.29 mA = 87.3 ohm
   B. 11.3 ohm
   C. 873 ohm
   D. 0.2 ohm
   Answer: A. I = 1 uA x (e^7.737 - 1) = 2.29 mA. (Key point: Static resistance)

4. Which formula and value give the dynamic resistance?
   A. r_d = V/I = 87.3 ohm
   B. r_d = I/V_T
   C. r_d = eta V_T/(I + I0) = 11.3 ohm
   D. r_d = V_T x I = 59 uohm
   Answer: C. It is the slope dV/dI at the operating point. (Key point: Dynamic resistance)

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