---
title: "Diode current and voltage, 0.1 V per decade"
subject: "Electronics Devices and Circuit"
chapter: 1
key: "semester_3/electronics_devices_and_circuit:diode-current-decade-drop"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/diode-current-decade-drop
site: BCT Engineering
---

# Diode current and voltage, 0.1 V per decade

Electronics Devices and Circuit · Chapter 1: Diodes

- Asked in: 2075 Ashwin, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/diode-current-decade-drop
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-1

## Question

Determine the current ID and the diode voltage VD with VDD=5 V and R= 1KΩ. Assume that the diode has a current of 1 mA at a voltage of 0.7 V and that its voltage drop changes by 0.1 V for every decade change in current.
[Figure: series circuit of VDD, resistor R and a diode, with current ID and diode voltage VD]

## Short answer

Using VD=0.7+0.1 log10(ID/1mA) and KVL ID=(5−VD)/1k, iteration converges to VD≈0.763 V and ID≈4.24 mA.

## Answer

The diode voltage changes by 0.1 V for every tenfold (decade) change in current, i.e. 

```text
VD = 0.7 + 0.1 log10(ID / 1 mA)
```
Together with KVL, ID = (VDD - VD)/R, solve by iteration.

#### Given
VDD = 5 V, R = 1 kΩ, VD = 0.7 V at 1 mA.

#### Iteration
| Step | VD guess (V) | ID = (5 - VD)/1 kΩ (mA) | New VD = 0.7 + 0.1 log10(ID) (V) |
|---|---|---|---|
| 1 | 0.700 | 4.300 | 0.7633 |
| 2 | 0.7633 | 4.237 | 0.7627 |
| 3 | 0.7627 | 4.237 | 0.7627 |

Converged.

```text
ID = (5 - 0.763)/1 kΩ = 4.24 mA
```

**Answer: ID ≈ 4.24 mA, VD ≈ 0.763 V.**

## Check yourself

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

1. What equation expresses 'voltage changes by 0.1 V per decade of current'?
   A. VD = 0.7 + 0.1 ID
   B. VD = 0.7 + 0.1 log10(ID/1 mA)
   C. VD = 0.1 + 0.7 log10(ID)
   D. VD = 0.7 x log10(ID)
   Answer: B. A tenfold current change gives 0.1 V, so a log10 relation. (Key point: Decade rule)

2. What is the second equation?
   A. ID = VDD + VD
   B. ID = VD/R
   C. ID = (VDD - VD)/R
   D. ID = VDD R
   Answer: C. KVL gives ID = (5 - VD)/1 kohm. (Key point: KVL)

3. Starting from VD = 0.7 V, what is the next VD?
   A. 0.7 V
   B. 0.9 V
   C. 0.80 V
   D. 0.7633 V
   Answer: D. ID = 4.3 mA, log10(4.3) = 0.633, so VD = 0.7633 V. (Key point: First iteration)

4. What is the final answer?
   A. ID = 4.30 mA, VD = 0.7 V
   B. ID = 2 mA, VD = 0.8 V
   C. ID = 5 mA, VD = 0
   D. ID = 4.24 mA, VD = 0.763 V
   Answer: D. Convergence gives VD = 0.7627 V and ID = 4.237 mA. (Key point: Result)

## Related in Electronics Devices and Circuit

- [Diode current and voltage, VDD 5 V, R 1 kΩ](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Adiode-current-vd-eta2) — Electronics Devices and Circuit, chapter 1
- [MOSFET ID and VDS (VDD 10 V, 6 kΩ, Vt=1 V)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Amosfet-id-vds-10m-6k) — Electronics Devices and Circuit, chapter 3, asked 7×
- [Diode circuit current, eta 1.74](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Adiode-current-eta-1p74) — Electronics Devices and Circuit, chapter 1, asked 4×
- [JFET ID and VDS (VP -5.5 V, IDSS 10 mA), pinch-off check](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-self-bias-vp-5p5) — Electronics Devices and Circuit, chapter 3, asked 3×
- [JFET ID and VDS (VP -3.5 V, IDSS 10 mA), pinch-off check](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-self-bias-vp-3p5) — Electronics Devices and Circuit, chapter 3, asked 3×
- [JFET ID and VDS (VP -5.5 V, IDSS 12 mA)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ajfet-self-bias-vp-5p5-idss12) — Electronics Devices and Circuit, chapter 3, asked 3×

## Related in other subjects

- [Zener circuit output voltage and current](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Azener-circuit-120v-5k) — Basic Electrical and Electronics Engineering, chapter 3
- [Thevenin: 4 kΩ resistor, 12 V, 10 mA](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Athevenin-12v-10ma) — Basic Electronics Engineering, chapter 1, asked 2×
- [Mesh analysis: voltage across 1 Ω resistor](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Amesh-analysis-dependent-source-1ohm) — Electrical Circuit Theory, chapter 1
- [Every RE has NFA; ε-NFA for bb(a∪b)*ab](https://www.bctengineer.com/question.md?key=semester_3%2Ftheory_of_computation%3Are-to-nfa-bb-aub-ab) — Theory of Computation, chapter 2