Series Circuit of a Resistor and a Capacitor

Background Information

The apparent resistance (impedance) of a capacitor depends on the frequency. The capacitive reactance is given by: $$X_{\rm C} = \frac {1}{ωC}$$
For a series connection of a resistor and a capacitor, the magnitude of the impedance is calculated as:
$$Z = \sqrt{R_{\rm 1}^2 + \frac{1}{(ωC_{\rm 1})^2}}$$

Experimental Tasks

1. Assemble the measurement circuit shown in figure 1:
   

   Fig. 1: Series Circuit of a Resistor and a Capacitor

   
   The corresponding phasor diagram is also illustrated in figure 1.
   

2. Adjust the function generator to output a sinusoidal voltage with a frequency of 6 kHz and an amplitude of 6 V.
3. Measure both the frequency and the amplitude using the oscilloscope.
   
   
4. Sketch the time-domain waveforms of the voltages $u_{\rm F}$ and $u_{\rm C}$, clearly indicating the phase shift between them.
   
   Fig. 2 Channel 1: $ \frac{V}{\rm DIV} = $
   
   Channel 2: $ \frac{V}{\rm DIV} = $
   
   Time basis: $ \frac{T}{\rm DIV} = $
   

1. Draw the phasor diagram with the measured values.
2. Calculate the impedance $Z$, the current amplitude $\hat{I}$, and the voltage amplitudes $\hat{U}_{\rm R}$ and $\hat{U}_{\rm C}$ based on the given component values $R_{\rm 1}$, $C_{\rm 1}$ and the source voltage amplitude $\hat{U}_{\rm F}$.
3. Compare the calculated results with the measured values.
   
   
   
   
   
   
4. Repeat this experiment using a capacitor with a capacitance of 1 µF
   
   Fig. 3 Channel 1: $ \frac{V}{\rm DIV} = $
   
   Channel 2: $ \frac{V}{\rm DIV} = $
   
   Time basis: $ \frac{T}{\rm DIV} = $
   

1. Draw the corresponding phasor diagram using the newly measured values:

Test questions - Series Circuit of a Resistor and a Capacitor