**Title: Calculating Rv for a d’Arsonval Voltmeter****Objective:**Determine the value of Rv for different full-scale readings in a d'Arsonval voltmeter.**Problem Statement:**For the given d'Arsonval voltmeter diagram, calculate the value of Rv for each of the following full-scale readings:- a) 100 V- b) 25 V- c) 500 mV- d) 5 mV**Diagram Explanation:**The diagram presents a d'Arsonval voltmeter with the following key components:- A series resistor Rv, whose value needs to be determined.- A galvanometer characterized by: - Full-scale voltage (Vg) of 10 mV - Full-scale current (Ig) of 0.2 mAThe voltmeter circuit includes:- A positive (+) and a negative (-) terminal.- Arrows indicating current (Iv) and voltage (Vv) across the meter.**Calculation Approach:**For a full-scale deflection, the voltage across the combination of the galvanometer and Rv should match the full-scale reading. The relationship can be expressed by the formula:\[ V_{\text{full-scale}} = (R_{\text{g}} + Rv) \times I_{\text{g}} \]Where:- \( V_{\text{full-scale}} \) is the target full-scale reading.- \( R_{\text{g}} \) is the internal resistance of the galvanometer.- \( I_{\text{g}} \) is the current needed for a full-scale deflection (0.2 mA in this case).By rearranging the formula, the value of Rv can be calculated as:\[ Rv = \frac{V_{\text{full-scale}}}{I_{\text{g}}} - R_{\text{g}} \]**Procedure:**1. Insert the values of the full-scale readings (100 V, 25 V, 500 mV, 5 mV) into the formula.2. Calculate Rv for each case assuming you know the internal resistance \( R_{\text{g}} \).This calculation is crucial for ensuring the voltmeter reads accurately at the requested full-scale settings by adjusting Rv appropriately.

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Answered: U. A d'Arsonval voltmeter is shown…

U. A d'Arsonval voltmeter is shown below. Find the value of Rv for each of the following full Scale Readings: a) 100 V b)25 V c) 500 mV d) 5 mV lv Rv 10 mV .2 mA

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

**Title: Calculating Rv for a d’Arsonval Voltmeter**

**Objective:**
Determine the value of Rv for different full-scale readings in a d'Arsonval voltmeter.

**Problem Statement:**
For the given d'Arsonval voltmeter diagram, calculate the value of Rv for each of the following full-scale readings:
- a) 100 V
- b) 25 V
- c) 500 mV
- d) 5 mV

**Diagram Explanation:**

The diagram presents a d'Arsonval voltmeter with the following key components:
- A series resistor Rv, whose value needs to be determined.
- A galvanometer characterized by:
- Full-scale voltage (Vg) of 10 mV
- Full-scale current (Ig) of 0.2 mA

The voltmeter circuit includes:
- A positive (+) and a negative (-) terminal.
- Arrows indicating current (Iv) and voltage (Vv) across the meter.

**Calculation Approach:**

For a full-scale deflection, the voltage across the combination of the galvanometer and Rv should match the full-scale reading. The relationship can be expressed by the formula:

\[ V_{\text{full-scale}} = (R_{\text{g}} + Rv) \times I_{\text{g}} \]

Where:
- \( V_{\text{full-scale}} \) is the target full-scale reading.
- \( R_{\text{g}} \) is the internal resistance of the galvanometer.
- \( I_{\text{g}} \) is the current needed for a full-scale deflection (0.2 mA in this case).

By rearranging the formula, the value of Rv can be calculated as:

\[ Rv = \frac{V_{\text{full-scale}}}{I_{\text{g}}} - R_{\text{g}} \]

**Procedure:**

1. Insert the values of the full-scale readings (100 V, 25 V, 500 mV, 5 mV) into the formula.
2. Calculate Rv for each case assuming you know the internal resistance \( R_{\text{g}} \).

This calculation is crucial for ensuring the voltmeter reads accurately at the requested full-scale settings by adjusting Rv appropriately.

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