Question

(a) What resistance would you put in parallel with a \(40.00 - \Omega \) galvanometer having a \(25.0 - \mu A\) sensitivity to allow it to be used as an ammeter that has a full-scale deflection for \(10.0{\rm{ }}\mu A\) ?

(b) What is unreasonable about this result?

(c) Which assumptions are responsible?

Short answer

(a) The total resistance of the parallel combination is \(R = - 66.67{\rm{ }}\Omega \).

(b) Since, the resistance is negative therefore, the result is unreasonable.

(c) The assumption of small-scale deflection and too rough sensitivity was incorrect and are responsible for unreason ability of the value obtained.Sensitivity is larger than full-scale deflection.

Step-by-step solution

Concept Introduction

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.

Information Provided

• Resistance in galvanometer:\(40.00 - \Omega \)
• Sensitivity in galvanometer:\(25.0 - \mu A\)
• Scale reading of ammeter:\(10{\rm{ }}\mu A\)

Resistance in the series

a.

A\(40.00 - \Omega \)galvanometer having a\(25.0 - \mu A\)sensitivity.

Total Resistance of the voltmeter can be calculated as:

\({R_{tot}} = (r)\left( {\frac{{{I_G}}}{{I - {I_G}}}} \right)\)

Substitute the values\(r = 40{\rm{ }}\Omega ,{\rm{ }}{I_G} = 25{\rm{ }}\mu A,{\rm{ }}I = 10{\rm{ }}\mu A\).

Resistance of resistor is calculated as –

\(\begin{align}{}R = (40{\rm{ }}\Omega )\left( {\frac{{25{\rm{ }}\mu A}}{{10{\rm{ }}\mu A - 25{\rm{ }}\mu A}}} \right)\\R = (40{\rm{ }}\Omega )\left( {\frac{{25 \times {{10}^{ - 6}}\;A}}{{10 \times {{10}^{ - 6}}\;A - 25 \times {{10}^{ - 6}}\;A}}} \right)\\R = - 66.67{\rm{ }}\Omega \end{align}\)

Therefore, the total resistance is \(R = - 66.67{\rm{ }}\Omega \).

Unreason ability

(b)

The value for the resistance obtained is\(R = - 66.67{\rm{ }}\Omega \).

The value of resistance can only be positive.

Therefore, the result is unreasonable.

Assumptions responsible

(c)

Wrong assumptions made regarding the situation was small scale deflection, too rough sensitivity.

Therefore, small scale deflection, too rough sensitivity resistance are the assumptions responsible.