Physics 109 - RC Circuits Part II

Time constants: Last week you gathered data that follows an exponential decay. A standard way to express the decaying voltage across the circuit is

V(t) = Vo exp(-t/tau)

where tau is referred to as the time constant. Note that a quick way to obtain an estimate of a time constant is to measure the time it takes for the voltage to fall to Vo/e .

RC Circuits Part II: Your next step in taking data is to uncover how the time constant of the exponential decay varies with the resistance R. Try measuring the time constant over a wide range of values of R. You will need to make quite a few measurements across a wide range of R from about 20 Ohms to 10,000 Ohms, try 6 measurements initially, using the shortcut mentioned above. Use a capaciatnce of 0.1 microfarads (the precision of the decade boxes is + 1%) throughout the measurements. The expected behaviour is tau = RC

Marking Scheme

detailed description of data-taking method, including how you detrmined uncertainty: 2 marks
high quality data set: 2 marks
weighted least squares fit to a log-log plot of the time constant versus R (graph plus copy of spreadsheet calculation): 2 marks
weighted least squares fit to a plot of time constant versus R: 2 marks
residuals plots: 1 mark
graph elements (Axis labels, uncertainty bars, fit lines etc.: 1 mark
conclusions: does the model for the time constant work? how well does the clope agree with the capaciatnce? 3 marks