---
title: "JFET ID and VDS (VP -5.5 V, IDSS 12 mA)"
subject: "Electronics Devices and Circuit"
chapter: 3
key: "semester_3/electronics_devices_and_circuit:jfet-self-bias-vp-5p5-idss12"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/jfet-self-bias-vp-5p5-idss12
site: BCT Engineering
---

# JFET ID and VDS (VP -5.5 V, IDSS 12 mA)

Electronics Devices and Circuit · Chapter 3: Field-Effect Transistor

- Asked in: 2070 Ashad, 2+2+2+2 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/jfet-self-bias-vp-5p5-idss12
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-3

## Question

Find ID and VDS for the given circuit. Given data are: VP = -5.5V, IDSS = 12 mA and assume all capacitors are ideal and check whether transistor is operating in pinch off region or not?
[Figure: n-channel JFET amplifier with VDD = 18 V; gate divider 1.5 MΩ from VDD to gate and 330 kΩ from gate to ground; 2 kΩ drain resistor; 1 kΩ source resistor with bypass capacitor C3; input coupling capacitor C1 and output coupling capacitor C2]

## Short answer

VG=3.246V, VGS=3.246−ID. Using ID=12(1−VGS/(−5.5))² gives ID=5.14mA, VDS=2.57V, but VDS< VGS−VP so not pinch-off. Ohmic region solution: ID≈5.07mA, VDS≈2.80V.

## Answer

**Given:** VDD = 18 V, R1 = 1.5 MΩ, R2 = 330 kΩ, RD = 2 kΩ, RS = 1 kΩ, VP = −5.5 V, IDSS = 12 mA. Capacitors are open at dc.

#### Gate voltage
VG = 18 × 330/(1500 + 330) = **3.246 V**

#### Step 1: assume pinch-off (saturation) (ID in mA, RS in kΩ)
VGS = VG − ID RS = 3.246 − ID

ID = 12 (1 − VGS/VP)² = 12 (1 + (3.246 − ID)/5.5)² = 12 (1.590 − 0.1818 ID)²

0.3967 ID² − 7.939 ID + 30.34 = 0

ID = 14.87 mA or 5.14 mA

ID = 14.87 mA is larger than IDSS (12 mA) and would give VGS = −11.6 V (beyond VP), which is impossible, so it is rejected.

ID = 5.14 mA, VGS = 3.246 − 5.14 = −1.90 V

VDS = VDD − ID (RD + RS) = 18 − 5.14 × 3 = 2.57 V

#### Step 2: check for the pinch-off region
For pinch-off (saturation) the JFET needs VDS ≥ VGS − VP:

VGS − VP = −1.90 + 5.5 = 3.60 V

VDS = 2.57 V < 3.60 V, so the condition is **not satisfied**. The JFET is **not in the pinch-off region**; it is in the ohmic (triode) region, and the saturation-equation values above are not exact.

#### Step 3: solve in the ohmic region
In the ohmic region the drain current is

ID = IDSS [2 (1 − VGS/VP)(VDS/|VP|) − (VDS/VP)²]

with VGS = 3.246 − ID and VDS = 18 − 3 ID. Solving this numerically (trial and error):

ID ≈ 5.07 mA, VGS ≈ −1.82 V, VDS = 18 − 3 × 5.07 ≈ 2.80 V

Check: VGS − VP = −1.82 + 5.5 = 3.68 V > VDS = 2.80 V, so the ohmic-region assumption is consistent. (As expected, the actual ID is slightly smaller, and VDS slightly larger, than the saturation-equation estimate.)

**Answer: ID ≈ 5.07 mA, VDS ≈ 2.80 V (VGS ≈ −1.82 V). Since VDS < VGS − VP, the transistor is not in the pinch-off region; it operates in the ohmic region. (The saturation equation alone gives ID ≈ 5.14 mA, VDS ≈ 2.57 V, which fails this check.)**

## Check yourself

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

1. Why is ID = 14.87 mA rejected?
   A. It exceeds IDSS = 12 mA
   B. It is not positive
   C. It is below 5 mA
   D. It exceeds VDD
   Answer: A. A JFET cannot carry more than IDSS in its normal range. (Key point: Rejecting a root)

2. With ID = 5.14 mA, RD = 2 kΩ, RS = 1 kΩ, VDD = 18 V, VDS is:
   A. 2.57 V
   B. 7.7 V
   C. 18 V
   D. 10.3 V
   Answer: A. VDS = 18 - 5.14*3 = 2.57 V. (Key point: VDS)

3. VDS = 2.57 V and VGS - VP = 3.60 V. What is the conclusion?
   A. VDS < VGS - VP, so the JFET is not in pinch-off but in the ohmic region
   B. In pinch-off
   C. Cut off
   D. Breakdown
   Answer: A. Pinch-off needs VDS >= VGS - VP, which fails, so the saturation-equation result is only approximate. (Key point: Pinch-off conclusion)

## Close variants set in other exams

- [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×

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