91Ó°ÊÓ

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.

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

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 \(R = 3{\rm{ }}M\Omega \).

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 \(R = 2.99{\rm{ }}k\Omega \).