Chapter 3, Problem 3.1P

To determine

The range of the voltmeter for the input range of mass from 1 to 10 kg, if the static sensitivity is 2 V/kg. Also, state the significance of increasing the static sensitivity.

Answer to Problem 3.1P

The range of the voltmeter should be:

$2\le V\left(\text{Volts}\right)\le 20$

The function of this electronic device is $V\left(m\right)=K\cdot m$, where static sensitivity represents the slope for this function. Thus, if the sensitivity is increased then the slope of this curve also increases or say for input A, the voltmeter produces the output equal to K times the input A.

Explanation of Solution

Given:

The static sensitivity of the electronic scale is 2 V/kg.

The input range of the voltmeter is 1 to 10 kg.

Concept Used:

The static sensitivity is the ratio of the magnitude of output to the input:

Let us assume a function of the form $y\left(t\right)=Kf\left(t\right)$

Then K is the sensitivity of this zero-order system. That is, for every unit of the input function, the output of the system is K times the input.

Calculation:

Since, the voltage measured by the voltmeter is a function of mass such that its static sensitivity is 2 V/kg.

Therefore, the function for the device can be defined as:

$V\left(m\right)=K\cdot m$

Where, m (kg) is the mass to be measured and K (V/kg) is the static sensitivity of the system.

For the given case, the range of input mass is:

$1\le m\left(\text{kg}\right)\le 10$

Therefore, the lower range of the voltmeter corresponding to input lower range 1 kg is:

$\begin{array}{l}V\left(m\right)=K\cdot m\\ \Rightarrow V\left(1\right)=2\cdot 1\because K=2\text{V/kg,}m=1\text{kg}\\ \Rightarrow V\left(1\right)=2\text{Volts}\end{array}$

Similarly, the upper range of the voltmeter corresponding to input upper range 10 kg is:

$\begin{array}{l}V\left(m\right)=K\cdot m\\ \Rightarrow V\left(10\right)=2\cdot 10\because K=2\text{V/kg,}m=10\text{kg}\\ \Rightarrow V\left(10\right)=20\text{Volts}\end{array}$

Therefore, the range of the voltmeter should be:

$2\le V\left(\text{Volts}\right)\le 20$

Also, the function of this electronic device is $V\left(m\right)=K\cdot m$, where static sensitivity represents the slope for this function. Thus, if the sensitivity is increased then the slope of this curve also increases, or say for input A, the voltmeter produces the output equal toK times the input A.

Conclusion:

The range of the voltmeter should be:

$2\le V\left(\text{Volts}\right)\le 20$

The function of this electronic device is $V\left(m\right)=K\cdot m$, where static sensitivity represents the slope for this function. Thus, if the sensitivity is increased then the slope of this curve also increases or say for input A, the voltmeter produces the output equal to K times the input A.