An electrical capacitor with an unknown capacitance is connected to the circuit shown. The switch is first connected to B and the capacitor is charged. Then, the switch is connected to A and the capacitor discharges through the resistor. As the capacitor is discharging, the voltage across the capacitor is measured for 10 s in intervals of 1 s. The recorded measurements are given in the table below.

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Chapter1: Introduction
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B
R=2000 2
ww
An electrical capacitor with an unknown capacitance is
connected to the circuit shown. The switch is first connected
to B and the capacitor is charged. Then, the switch is
connected to A and the capacitor discharges through the
resistor. As the capacitor is discharging, the voltage across the
capacitor is measured for 10 s in intervals of 1 s. The recorded
measurements are given in the table below.
Vo
3
t(s)
V (V)
1
4
5
6
7
10
9.4
7.31
5.15
3.55
2.81
2.04
1.26
0.97
0.74
0.58
You recall from PHYS2102 that the voltage of the capacitor, đuring a discharge, as function of time is
given by
V = V e-+/(RC)
This exponential equation can be written as a linear equation of In(V) and t in the form:
-1
In(V) :
t + In(Vo)
RC
Use Matlak to do the following:
*In all graphs add title, legend and axis labels
1. Estimate the time at which the voltage V=6.5 V.
2. Estimate, using spline interpolation, the voltage V1 corresponding to 30 times varying from 1 to
105.
3. In the same figure (3rª subplot), plot the experimental voltage data as blue diamond and the
interpolated voltage as solid magenta line.
4. Plot in the 4th subplot In(V) vs t as red squares.
5. Use linear fitting of In(V) vs t, and plot in the same 4º subplot, the fitting curve as black solid
line.
6. Use sprintf to report in the previous figure the intercept and slope of the linear fit
Transcribed Image Text:B R=2000 2 ww An electrical capacitor with an unknown capacitance is connected to the circuit shown. The switch is first connected to B and the capacitor is charged. Then, the switch is connected to A and the capacitor discharges through the resistor. As the capacitor is discharging, the voltage across the capacitor is measured for 10 s in intervals of 1 s. The recorded measurements are given in the table below. Vo 3 t(s) V (V) 1 4 5 6 7 10 9.4 7.31 5.15 3.55 2.81 2.04 1.26 0.97 0.74 0.58 You recall from PHYS2102 that the voltage of the capacitor, đuring a discharge, as function of time is given by V = V e-+/(RC) This exponential equation can be written as a linear equation of In(V) and t in the form: -1 In(V) : t + In(Vo) RC Use Matlak to do the following: *In all graphs add title, legend and axis labels 1. Estimate the time at which the voltage V=6.5 V. 2. Estimate, using spline interpolation, the voltage V1 corresponding to 30 times varying from 1 to 105. 3. In the same figure (3rª subplot), plot the experimental voltage data as blue diamond and the interpolated voltage as solid magenta line. 4. Plot in the 4th subplot In(V) vs t as red squares. 5. Use linear fitting of In(V) vs t, and plot in the same 4º subplot, the fitting curve as black solid line. 6. Use sprintf to report in the previous figure the intercept and slope of the linear fit
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