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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Find the resistance that must be placed in series with a $$10.0 - \Omega$$ galvanometer having a $$100 - \mu A$$ sensitivity to allow it to be used as a voltmeter with: (a) a $$300 - V$$ full-scale reading, and (b) a $$0.300 - V$$ full-scale reading.

(a)The resistance that must be placed in series with a $$10.0 - \Omega$$ galvanometer having a $$100.0 - \mu A$$ sensitivity to allow it to be used as a voltmeter with $$300 - V$$full-scale readingis, $$R = 3{\rm{ }}M\Omega$$.

(b)The resistance that must be placed in series with a $$10.0 - \Omega$$ galvanometer having a $$100.0 - \mu A$$ sensitivity to allow it to be used as a voltmeter with $$0.300 - V$$full-scale readingis, $$R = 2.99{\rm{ }}k\Omega$$.

See the step by step solution

## Step 1: Concept Introduction

A galvanometer is an electromechanical device used to detect electric current. A galvanometer deflects a pointer in response to an electric current flowing through a coil in a constant magnetic field. An example of an actuator is a galvanometer.

The total flow of electrons via a wire can be used to describe the rate of electron flow. Anything that prevents current flow is referred to as "resistance." An electrical circuit needs resistance in order to transform electrical energy into light, heat, or movement.

## Step 2: Information Provided

• Inner resistance in galvanometer: $$10.0 - \Omega$$
• Sensitivity of galvanometer: $$100.0 - \mu A$$
• Scale measure of voltmeter: $$300 - V$$
• Scale measure of voltmeter: $$0.300 - V$$

## Step 3: Calculation for Resistance

a.

A galvanometer in a voltmeter with inner resistance:$$10.0 - \Omega$$

A galvanometer in a voltmeter with sensitivity:$$100.0 - \mu A$$

Full scale reading of voltmeter: $$300 - V$$

Calculate the additional resistance $${\rm{R}}$$, connected in series to the internal resistance, necessary for the galvanometer tohave $${V_a} = 300 - V$$full-scale reading. The total resistance in this case is $$r + R$$.Calculate $$R$$ as –

\begin{align}{}r + {R_a} & = \frac{{{V_a}}}{I}\\{R_a} & = \frac{V}{I} - r\\ & = \frac{{300\;V}}{{100{\rm{ }}\mu A}} - 10{\rm{ }}\Omega \end{align}

\begin{align}{} &= 2999990{\rm{ }}\Omega \\ &= 3{\rm{ }}M\Omega \end{align}

Therefore, the value for resistance is obtained as $$R = 3{\rm{ }}M\Omega$$.

## Step 4:Calculation for Resistance

b.

A galvanometer in a voltmeter with inner resistance:$$10.0 - \Omega$$

A galvanometer in a voltmeter with sensitivity:$$100.0 - \mu A$$

Full scale reading of voltmeter: $$0.300 - V$$

Calculate the additional resistance $$R$$, connected in series to the internal resistance, necessary for the galvanometer tohave $${V_b} = 0.300 - V$$full-scale reading. The total resistance in this case is $$r + R$$.Calculate $$R$$ as –

\begin{align}{}r + {R_b} & = \frac{{{V_b}}}{I}\\{R_b} & = \frac{V}{I} - r\\ & = \frac{{0.300\;V}}{{100{\rm{ }}\mu A}} - 10{\rm{ }}\Omega \end{align}

\begin{align}{} & = 2990{\rm{ }}\Omega \\ & = 2.99{\rm{ }}k\Omega \end{align}

Therefore, the value for resistance is obtained as $$R = 2.99{\rm{ }}k\Omega$$.