Question

Resistor - 100 mega-ohms

capacitor - .47 micro farads

i am having an extremely hard time finding the theoretical time constant and the experimental ones.

Format Painter 龘· . ▼ 窖三三一嚚 Merge & Center s-90 , Clipboard Font Alignment Number 0 2.81 7.8 15.4 25.76 0 0.5 1 1.5 Charging a Capacitor 38.732.5 2 54.95 74.26 97.67 124.45 156.24 193.33 235.43 284.47 3.5 4 4.5 5.5 50 100 150 Time (s) 6.5 seconds voltage seconds voltage 10 9.5 Discharging a Capicitator 2.59 7.61 284.47 6.5 econds voltage Time (s) seconds voltage 10 9.5 9 8.5 Discharging a Capicitator 2.59 7.61 15.36 25.81 39.27 55.87 76.26 100.24 128.16 160,46 197.69 240.65 289,48 12 10 7.5 6.5 6 5.5 P 4 4.5 4 3.5 50 100 150200 250 300 350 400 Time (s) 345.5 Charging a Capacitor 35 Sheetl .3.1 Data Analysis 1. Transfer your data for the large time constant to Excel. 2. Plot the voltag e Vo across the capacitor as a function of time for both the charging and discharging data. Include appropriate labels for the title and axes of each graph. You will have four separate graphs for this step. 3. Determining the experimental time constant. Method 1: The time constarnt T RC is the time for the capacitor to charge to within (1/e)th of its full charge for the given voltage (that is, Ve = 0.63216), or the time for the capacitor to discharge to (1/e)th of it initial value (that is, le 0.36%). Print the graphs from the last step and use each graph to approximate the time constant by identifying the point on the graph when the voltage is at the appropriate value. You may need to interpolate between data points. Clearly label the point you used on each graph. 4. Determining the experimental time constant. Method 2: Plot In(Vo) versus t for the discharging data. Is this nearly a straight line? Why? Add a linear equation of best fit to the graph and display the equation on the graph. Use the equation to ydetermine the time constant τ = RC 2.3 Large time constant L'e- pc:1100x10%47K(0-o) Theoretical time constant: . Experimental time constant [ Graph 1 Charging graph Discharging graph Time Constant Percent Error 31 92 1S vs t Linear equation of best fit for In(Vc) vs t

Answer 1

Hi,

I also noticed the large discrepancy between the theoretical time constant (which you have correctly computed to be 47sec, and the experimentally observed value of around 250 second. I assume that you are looking for some explanation for this. If that be the case here are some potential sources of error:

1 Type of capacitor used. If it is a ceramic capacitors then tolerance of 20% or sometimes even higher are common. Temperature variations also affect the value of ceramic capacitors quite a bit.

2 Tolerance on resistance: This should be around 5% for carbon-film resistors typically but a bad component does occasionally creep in. In case you have the option of measuring the value of resistor with a digital multimeter, please do not touch the resistor leads when its value is being measured.

3. Sometimes a wrong value of component get used, accidently. So please cross-check, if you can, whether 0.47microfarad and 100megaohm were the ones actually used.

Now coming to the last part, i.e. Ln(Vc) versus t graph. The graph is given in the image below:

This is nearly a straight line. Its equation can be derived from capacitor discharging equation:

In(vc) 0 2.302585093 2.59 2.251291799 7.61 2.197224577 5.36 2.140066163 25.81 2.079441542 9.27 2.014903021 55.87 1.945910149 76.26 1.871802177 100.24 1.791759469 128.16 1.704748092 160.46 1.609437912 197.69 1.504077397 240.65 1.386294361 289.48 1.252762968 45.5 1.098612289 Ln(Vc) versus t 4 2.5 2 2 2 0.5 0 50 100 50 200 250 300 350 400

Vc = 10*exp(-t/tc) where tc = time constant

taking ln on both side

ln(Vc) = ln(10) - t/tc

So -1/tc is the slope of the line, and ln(10) is the y-axis intercept

Therefore

ln(Vc) = 2.3-0.00373t

As expected, this graph also indicates the time constant is around 268seconds.

Hope this helps in some manner.