# Step 1

- Construct the circuit in the diagram below:

- Here is a picture of the testbench setup:

- And here is a more detailed view of the circuit on the breadboard:

- In this setup R1 has a very large value to create an almost constant current source that charges the capacitor, and R2 is used to indirectly probe the current flow through the capacitor.

# Step 2

- Connect Channel 1 of the oscilloscope to node B of the circuit and Channel 2 to node C, as shown in the diagram below:

- Set the function generator to rectangular wave of about 5V amplitude and about 200Hz frequency.

- Configure Channel 1 settings to 200mV/div and Channel 2 to 20mV/div.

- Set the oscilloscope time base to 1ms/div.

- Configure the oscilloscope trigger source to Channel 1, rising edge, and adjust the level to be within the signal range.

- With these settings the oscilloscope should display two waveforms similar to the screenshot below:

- In this picture channel 1 (yellow trace) represents the voltage on the capacitor, and channel 2 (blue trace) represents the voltage drop on R2=1kOhm. This voltage can be converted into the current flowing through the capacitor during the charging and discharging phases. Notice the charging current is positive (about 20mV/1k = 20uA).

- Insert a screenshot of the displayed waveforms in this step.

- Why the voltage on the capacitor varies linearly during charging and discharging phases?

# Step 3

- Use the built-in cursor functions of the oscilloscope to measure the slope of the voltage variation on the capacitor during the charging phase, as shown in the screenshot below:

- In the example shown above delta V = 504mV and delta T = 2.68ms.

- Insert a screenshot of the oscilloscope displayed waveforms and cursor readings.

- Determine the value of the charging and discharging current from the voltage drop on R2 displayed by Channel 2 waveform.

- From the delta V and delta T measurements in your experiment derive the value of the charging current using the equations presented in the Theory section of the lab.

- Compare the calculated current with the measured current and comment on the result.

# Step 4

- Construct the circuit in the diagram below:

- Here is a detailed view of the circuit on the breadboard:

- In this setup the capacitor charges and discharges through the resistor R1 (100Ohms) and the resistor R2 (1 Ohms) is used to probe the current flowing through the capacitor during the charging and discharging phases.

# Step 5

- Connect Channel 1 of the oscilloscope to node B of the circuit and Channel 2 to node C, as shown in the diagram below:

- Set the function generator to rectangular wave of about 10V amplitude and about 200Hz frequency.
- Configure Channel 1 settings to 2V/div and Channel 2 to 100mV/div.
- Set the oscilloscope time base to 10us/div.
- Configure the oscilloscope trigger source to Channel 1, rising edge, and adjust the level to be within the signal range.

- With these settings the oscilloscope should display two waveforms similar to the screenshot below:

- In this picture channel 1 (yellow trace) represents the voltage on the capacitor, and channel 2 (blue trace) represents the voltage drop on R2=1Ohm. This voltage can be converted into the current flowing through the capacitor during the charging and discharging phases.

- Insert a screenshot of the displayed waveforms in this step.

- Why the voltage on the capacitor does not vary linearly during charging and discharging phases like it did in steps 1-3?

# Step 6

- Use the built-in cursor functions of the oscilloscope to measure the time constant of the voltage variation on the capacitor during the charging phase, as shown in the screenshot below:

- In the example shown above cursor 1 has been placed at the beginning of the charging phase and cursor 2 has been placed so that delta V = 7.04V, which is close to 0.707*10V amplitude. With these settings, delta T = 18.4us represents the time constant of the circuit, which theoretically should be equal to R*C. If we multiply R*C = 100Ohms*100nF = 10us; however, notice that the measured value is larger = 18.4us. The difference comes from the output impedance of the function generator, which is equal to 50 Ohms. Adding 50 Ohms we calculate 15us, which is close to the measured 18us.

- Insert a screenshot of the oscilloscope displayed waveforms and cursor readings.

- From the delta V and delta T measurements in your experiment determine the measured time constant of the circuit.

- Calculate the time constant and compare the result with the measured value. Comment on any discrepancy between calculated and measured values.