A circuit you\'re using discharges a 20- Fcapacitor through an unknown resistor.
ID: 1343646 • Letter: A
Question
A circuit you're using discharges a 20-Fcapacitor through an unknown resistor. After charging the capacitor, you close a switch at t=0 s and then monitor the resistor current with an ammeter. Your data are as follows:
Graphing either t versus ln(I) or ln(I) versus t gives a straight line. In the graph shown above, we chose to plot ln(I) on the vertical axis and t on the horizontal axis. From the equation for the line of best fit given, determine the resistance R.
Express your answer to two significant figures and include the appropriate units.
Time, t(s) Current, I(A) 0.5 890 1.0 640 1.5 440 2.0 270 2.5 200Explanation / Answer
apply inRC ckt
I = Io e^-t/RC
taking ln of both side,
ln(I/I0) = - t/RC
ln (I) - ln(I0) = - t/RC
ln(I) = - (1/RC) t + ln(I0)
comparing it with given equation,
ln (I ) = - 0.770t - 6.61
1/RC = 0.770
R = 1 / (0.770* 20 * 10^-6)
R = 64935.06 Ohm or 65 k Ohms
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