Write the equation for the function that describes the voltage across the capaci

Question

Write the equation for the function that describes the voltage across the capacitor
versus time below, including known values for all constant terms. Did the
exponential function fit your data well? Based on these results, can we say that the
decay of voltage across the capacitor is an exponential decay?

The equation in the box in the graph below is what I have to work with.

Write the equation for the function that describes the current through the resistor
versus time below, including know values for all constant terms. Did the
exponential function fit your data well? Based on these results, can we say that the
decay of current through the resistor is an exponential decay?

Find the value of the time constant, , from your function for the voltage across the capacitor versus time. Also calculate the theoretical value from the known values of capacitance and resistance, and determine the percent error between the experimental and theoretical values. Show your calculations below. Do your values agree to within experimental uncertainty? (Remember that your resistance and capacitance values are only known to within ±10%.)

18 1 1. Il 21-18 11-18 18 1 111 520320 00 D 000 D D ODD D 0DDD-00-D000000 ren 12 13 14 15 18 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 31

Explanation / Answer

form the graph
the plot is given by
y = Ae^(-Cx) + B
where A = 17.44
C = 0.4742
B = 5.035

now equation for a capacitor decay is given by
V(t) = Vo*e^(-t/RC)

hence by comparing coefficients
A = 17.44 V
1/RC = 0.4742
hence the plot did indeed follow an exponential decay

now, time constant = RC = 1/0.4742 = 2.108814 s
for any value of given resistance R and capacitance C
time constant = RC
and precent difference from experimental value = (1.108814 - RC)*100/RC

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