Help Please!!

I have a exam for my foundation year uni course tomorrow and it is likely a maths question like this will appear...... how do i go about it? im stumped!!!!

The resistance (R ohms) of a winding field is measured at various temperatures (t° C) and the results are recorded in the Table below:

t (° C) 21 26 33 38 47 54 59 66 75
R (ohms) 109 111 114 116 120 123 125 128 132

The law connecting R and t is of the form R = a + bt. Find suitable values of a and b.

Thanks :biggrin:

Reply 1

dknt

12

Original post by beckaboos.

I have a exam for my foundation year uni course tomorrow and it is likely a maths question like this will appear...... how do i go about it? im stumped!!!!

The resistance (R ohms) of a winding field is measured at various temperatures (t° C) and the results are recorded in the Table below:

t (° C) 21 26 33 38 47 54 59 66 75
R (ohms) 109 111 114 116 120 123 125 128 132

The law connecting R and t is of the form R = a + bt. Find suitable values of a and b.

Thanks :biggrin:

Well compare to the general equation for the straight line, y=mx +c

Reply 2

Maths Tutor

Plot the values on a graph (t on the x-axis and R on the y-axis).

Draw a straight line of best fit to 'join' the values (some will be above the line, some below)

Then take 2 sets of readings from the line of best fit to get 2 equations.

Solve the 2 equations simultaneously to find a and b.

As an approximation without using a graph, you could take 2 sets of readings from the values given and work as follows:

1st, when t=26, R=111

So the 1st equation is: 111 = a + 26b

2nd, when t=21, R=109

So the 2nd equation is: 109 = a + 21b

Now solve the simultaneous equations:

111 = a + 26b

109 = a + 21b

Subtracting the 2nd equation from the 1st: (We SUBTRACT because a is +ve in both equations and will disappear)

(111 - 109) = (a - a) + (26b - 21b)

2 = 0 + 5b

2 = 5b

Dividing both sides by 5:

2/5 = b

b = 2/5

b = 0.4

Knowing b, we can now find a:

109 = a + 21b

109 = a + 21(0.4)

109 = a + 8.4

Taking away 8.4 from both sides:

100.6 = a

a = 100.6

So a = 100.6 and b = 0.4

The equation now becomes:

R = 100.6 + 0.4t

Given any value of R, we can now find t, and given any value of t, we can now find R.

Let's see if the equation works.

From the table, when t=75, R=132

Putting these values in the equation:

132 = 100.6 + 0.4(75)

132 = 100.6 + 30

132 = 130.6

which is approximately correct.

(The more accurate your line of best fit, the more accurate your answers will be.)

Help Please!!

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