Question

2) a) A rectangular piece of paper of size 841 mm x 1189 mm (A0 size) is to be divided into 16 equal A4 sized sheets. What are the dimensions of one A4 size paper? b) Determine the weight of an A4 sheet made from 80 g/m2 paper. 3) The characteristics of a hydrogel-based pH sensor is given in table below. The output resolution of this sensor is 0.005 mV. Input (ph) 0 1 23 4 56 7 89 10 11 12 13 14 02.252.252.2522.5 3 3.5 44.5 5 5.5 66.25 6.25 6.25 (mV) The ph values of some liquids: Distilled water (7.0), Acids (0-7), Alkalines (7-14) Milk (6.6), Coffee (5.0), Beer (4.4) Orange juice (3.7), Fruit vinegar (3.2), Cola beverages (2.8) (a) Plot output Vo vs input ph (b) Determine input range and span (c) Determine output range and span (d) What is the "ideal" (linear) operation range of this sensor? (e) Determine the line equation that represents the input-output relationship over the operating range in (d (f) Determine sensitivity (g) Considering the entire pH range and using the equation you got in part (d), at what pH value does the sensor exhibit maximum nonlinearity?

Answer 1

3)

Solution:

Part :a

Plot of Vo vs ph is given below.

ph vs Output Voltage (mV) plot 10 12 13 14 ph.

Part:b

Input Range=0-14 ph

Input Span=14 ph

Part:c

Output Range=2-6.25 mV

Output Span=4.25 mV

Part:d

Linear operating range (from the graph) = 3-11 ph

Part:e

To find the equation of line which is

$y=mx+c$, where m is the slop and c is the point where line cuts the y-axis.

now,

2-1 T2-1

i am selecting 2 points as

(x1,y1)=(3,2)

(x2,y2)=(11,6)

so

,

6-2 m= 11-3

m=0.5

now for "c",

take any point on the line like, (x,y)=(5,3)

so

$y=mx+c$

(0.5)(5) + C 3

solving this for "c" we got,

$c=0.5$

hence equation of line will be as,

y-0.5x 0.5

Part:f

sensitivity is given as,

Unit change in output sensitivityUnit change in input

so

2.5- 2 sensitivity 43

hense,

sensitivity 0.5

bias - 0

Part:g

input resolution is given by the formula,

$input \:resolution=\frac{output\:resolution}{Sensitivity}$

0.005 0,5 input resolution

$\mathbf{input \:resolution=0.01\:ph}$

Part:h

For this i have made 2 graphs on one window, 1st is the extended linear graph from part d and 2nd is the actual graph, this is shown in below figure,

Comparison of Ideal and Actual Graph 3- 12

it is clearly visible that at "ph=0" sensor showed the maximum non linearity which is "1.75mV"