Question

1. a Calculate the natural log of the capacitor voltage for each time point

b. Add a linear trendline to your graph and display the best fit equation

c. Record the slope from your best-fit equation in step

d. Calculate the capacitor time constant τ using the slope with the equation

e. Calculate the internal DMM resistance R using the following equation:

( I am not sure how to use my data to answer this problem)

Voltage -2.28
-0.9
-0.75
-0.59
-0.46
-0.36
-0.28
-0.21
-0.16
-0.13
-0.09
-0.07
-0.05
-0.03
-0.02
-0.01

Time (in seconds) 0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160

Answer 1

1) a

Capacitor voltage(V ) Natural log of capacitor voltage

-2.28	0.82
-0.9	-0.10
-0.75	-0.28
-0.59	-0.52
-0.46	-0.77
-0.36	-1.02
-0.28	-1.27
-0.21	-1.56
-0.16	-1.83
-0.13	-2.04
-0.09	-2.40
-0.07	-2.65
-0.05	-2.99
-0.03	-3.50
-0.02	-3.91
-0.01	-4.60

Note that while calculating natural log insert positive value of capacitor voltage.You have got negative reading for voltage on your DMM because you have interchanged the positive and negative terminals.However magnitude remains the same.

b)Linear trendline to graph and the best fit equation is shown in the graph below for graph of natural logaritm of capacitor voltage vs time.

c)Slope of this graph is shown in the graph above.Slope is negative because as with increase in time we find that the capacitor voltage is decreasing.

d)Time constant can be found using the fact that time constant for an RC circuit is the time taken for the capacitor voltage to fall to 0.3629 times its final value.

e)Capacitor time constant is related to resistance by the relation

τ=RC

Where R is the resistance

C is the capacitance

Therefore substituting the value of capacitance we can get the value of resistance.