In this lab, we will determine the use of the capacitor by connecting it with a resistor to find its voltage. We will describe the fluctuations of the input square wave and its applications. We will determine the use of KVL in a capacitor circuit and apply DC offset to a circuit operating under a function generator.

Graphs are on the following pages.

1) tau = RC = (2200 ohm)(0.01µF) = 2.2 x 10^-5

Vs = RC (dVc/dt) + Vc

Vc (t) = -V0 + (Vc2 + V0) ^ [ - (t - T/2)/tau ] for T/2 < t < T

Vc (t) = - 2 V

Vc (t) = V0 + (Vc1 - V0) ^ [ - t/tau ] for 0 < t < T/2

Vc (t) = 2 V

Vr (t) = 4 V for T/2 < t < T

Vr (t) = 1 V for 0 < t < T/2

2) R = 2192 ohms

C = 0.010 µF

tau = RC = 2.192 x 10^-5

3) f = 10 kHz at 5 V amplitude with no DC offset.

Comparing with our analysis, ……

KVL does apply in the circuit. When we measure whole circuit, the amplitude from peak to peak was 5 V with a frequency of 100 µs.

4) When we increase the amplitude of the input square wave, the shape of the voltage stretches into positive and negative voltages, thus the voltage increases. Since the amplitude is the voltage, the voltage increases. So the peak to peak voltage stretches, indicating increased voltage.

5) In negative offset voltage, the voltage will show a more negative reading. When the offset is more positive, there is more voltage and the graph becomes much straighter.

6) Apparently, when we decrease the input frequency, the voltage increases from peak to peak, according to our sketch. The shape of the graph still remains the same.

7) When we increase the input frequency, the voltage in the capacitor decreases from peak to peak. The shape of the graph, however, remains the same, but with smaller frequency and more voltage.

Graphs are on the following pages.

1) f = 10 kHz at 5 V

Vc = 2.84 V to -2.84 V of sinusoidal form

Vr = 2.05 V to -2.04 V of sinusoidal form

Vc = (VwRC/(1 + w²(RC)²)) sin wt + (V/(1 + w²(RC)²)) cos wt

Vc1 = Vc (T) = - Vo + (Vc2 + Vo) e^(-tau/2T)

Vc1 cos (wt + ø) = - Vc2 = - Vo ((1- e^(-tau/2T))/(1- e^(-tau/2T))

2) Yes, KVL does apply in the circuit. The resistor and capacitor voltages combine to form a 5 V peak to peak voltage.

3)

The RC circuit can be used for finding the linear relationship of the voltage through the device with time. This can let to function for energy storing more efficiently in certain electronic devices.

4) When we increase the frequency, the period of the graph decreases, as with the voltage increases in both the capacitor and the input voltage. The phase shift at low frequencies is at 60 degrees. At high frequencies, the phase swift is at 30 degrees. The phase shift is exactly 45 degrees when the frequency is at 25 kHz.

5) In negative offset voltage, the voltage will show a more negative reading. When the offset is more positive, there is more voltage and the graph becomes much straighter.

In this lab, we learned that the frequency and the voltage are inverse proportional to each other by looking at different frequencies and voltages of a capacitor and resistor. We also learned that the capacitor acts as an open circuit in certain points in the sinusoidal form of the circuit. We learned that the input voltage can create an input signal among the DC offset, causing an increase or decrease in frequency.