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Charging and Discharging a Single Capacitor

RC Circuit: Charging and Discharging a Single Capacitor

We wish to make plots of the time-dependent behavior of capacitor voltage and current of the circuit. Take ten t, VC, and i(t) data points from the simulation. For the voltage plots, we wish to investigate what occurs when the capacitor is charging/discharging after closing a switch. Be sure to follow the conventions that are defined in section 2 of the lab manual – this should ensure what quantities go on each respective axis.

Voltage plots:

1. Using data from the simulation for the capacitor charging, plot the following:

Charging and Discharging a Single Capacitor img1

2. Using data from the simulation for the capacitor discharging, plot the following:

Charging and Discharging a Single Capacitor img2

Current plots:

3. Using data from the simulation for the capacitor charging, plot the following:

Charging and Discharging a Single Capacitor img3

Show that the calculation of ?? agrees with the given values for resistance and capacitance in the circuit by considering the following:

4. Fitting the semi-log plots of v(t) and i(t) on the spreadsheet. After fitting the data with a trendline, we can extract the slope and comment on how this will be used to determine the time constant, ??.

I [mA]

VC (V)

45.441

0.066

30.561

1.682

20.021

2.827

13.228

3.558

8.819

4.043

5.775

4.373

3.884

4.578

2.544

4.724

Charging and Discharging a Single Capacitor img4

The semi-log slope of Vc and Ic has to be 1 but the experimental slope is almost 1, so we have to find time constant from Vc and Ic separately after that we have to average these two values.

From the equation 1/time_constant = Slope of this plot - charging

Charging and Discharging a Single Capacitor img5

From the equation 1/time_constant = Slope of this plot – Charging

Charging and Discharging a Single Capacitor img6

Measurement of t1/2 and calculation of ??. In a few sentences, describe how your experimental (simulation) value of ?? corresponds to the actual value.

I use the slope of the voltage and current value for finding time constant.

Time Constant value is between 10-3/0.0413 and 10-3/0.0413

10-3/0.0413 = 0.02421

10-3/0.0413 = 0.02421

Average value of ?? is 0.02421

Charging and Discharging a Single Capacitor img7

Average value of t1/2  is 0.016781

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