A circuit you\'re using discharges a 20-?Fcapacitor through an unknown resistor.

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: Time, t(s) Current, I(?A) 0.5 890 1.0 640 1.5 440 2.0 270 2.5 200 Part B 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.

Explanation / Answer

when capacitor discharge through resistor.

I = I0 [ e^(- t/RC)]

I/I0 = 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 x 20 x 10^-6) = 64935.06 Ohm

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