## 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

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