Question

Suppose you have a \(40.00 - \Omega \) galvanometer with a \(25.0 - \mu A\) sensitivity.

(a) What resistance would you put in series with it to allow it to be used as a voltmeter that has a full-scale deflection for \(0.500{\rm{ }}mV\)?

(b) What is unreasonable about this result?

(c) Which assumptions are responsible?

Short answer

(a) The total resistance of the series is \(R = - 20{\rm{ }}\Omega \).

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

(c) The assumption of small-scale deflection and high galvanometer resistance was incorrectand are responsible for unreason ability of the value obtained.

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 voltmeter:\(0.500{\rm{ }}mV\)

Resistance in the series

a.

A \(40 - \Omega \) galvanometer having a \(25 - \mu A\) sensitivity.

Total Resistance of the voltmeter can be calculated as:

\({R_{tot}} = \frac{V}{I}\)

On substituting the values –

\(\begin{align}{}{R_{Total{\rm{ }}}} & = \frac{{0.500{\rm{ }}mV}}{{25{\rm{ }}\mu A}}\\{R_{Total{\rm{ }}}} &= \frac{{0.500 \times {{10}^{ - 3}}\;V}}{{25 \times {{10}^{ - 6}}\;A}}\\{R_{Total{\rm{ }}}} = 20{\rm{ }}\Omega \end{align}\)

As per Ohm's law, the total resistance is equal to the sum of internal resistance of galvanometer and resistance placed in series with the internal resistance. Thus, it can be written –

\({R_{Total{\rm{ }}}} = R + r\)

Now, \(r = 40{\rm{ }}\Omega \) and \({R_{Total{\rm{ }}}} = 20{\rm{ }}\Omega \).

Resistance of resistor is calculated as –

\(\begin{align}{}20{\rm{ }}\Omega & = R + 40{\rm{ }}\Omega \\R &= 20{\rm{ }}\Omega - 40{\rm{ }}\Omega \\R &= - 20{\rm{ }}\Omega \end{align}\)

Therefore, the total resistance is \(R = - 20{\rm{ }}\Omega \).

Unreason ability

(b)

The value for the resistance obtained is\(R = - 20{\rm{ }}\Omega \).

The value of resistance can only be positive.

Therefore, the result is unreasonable.

Assumptions responsible

(c)

Wrong assumption made regarding the situation was small scale deflection, large galvanometer resistance.

Therefore, small scale deflection, large galvanometer resistance are the assumptions responsible.