How did they solve for Vout? What are the steps they used? ## Solving for Output Voltage (\( V_{\text{out}} \))The equation given is:\[\frac{V_{\text{in}} - V_{\text{out}}}{R_1} = \frac{V_{\text{out}} - V_{D,\text{on}}}{R_2}.\]The annotation next to this equation asks, "How to solve for \( V_{\text{out}} \)?"### Derivation:To solve for \( V_{\text{out}} \), it follows that:\[V_{\text{out}} = \frac{\frac{R_2}{R_1} V_{\text{in}} + V_{D,\text{on}}}{1 + \frac{R_2}{R_1}}.\]This formula helps in evaluating the output voltage based on the input voltage, \( V_{\text{in}} \), diode forward voltage, \( V_{D,\text{on}} \), and the resistances \( R_1 \) and \( R_2 \).Please note that the explanation is augmented with basic algebraic manipulation to isolate \( V_{\text{out}} \) from the initial equation, following the rules of proportion and fraction arithmetic.

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Answered: Vin – Vout Vout – VD.on - R1 R2 How to…

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Vin – Vout Vout – VD.on - R1 R2 How to solue for Vout It follows that R2 Vin + V D.on R1 R2 1+ R1 Vout

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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How did they solve for Vout? What are the steps they used?

## Solving for Output Voltage (\( V_{\text{out}} \))

The equation given is:

\[
\frac{V_{\text{in}} - V_{\text{out}}}{R_1} = \frac{V_{\text{out}} - V_{D,\text{on}}}{R_2}.
\]

The annotation next to this equation asks, "How to solve for \( V_{\text{out}} \)?"

### Derivation:

To solve for \( V_{\text{out}} \), it follows that:

\[
V_{\text{out}} = \frac{\frac{R_2}{R_1} V_{\text{in}} + V_{D,\text{on}}}{1 + \frac{R_2}{R_1}}.
\]

This formula helps in evaluating the output voltage based on the input voltage, \( V_{\text{in}} \), diode forward voltage, \( V_{D,\text{on}} \), and the resistances \( R_1 \) and \( R_2 \).

Please note that the explanation is augmented with basic algebraic manipulation to isolate \( V_{\text{out}} \) from the initial equation, following the rules of proportion and fraction arithmetic.

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