
In this lab, we investigate the frequency response of the circuit shown in Figure 1. The circuit is energized by a sinusoidal voltage v(t). The output voltage is V_{o}, the voltage across the capacitor. The circuit forms a lowpass filter. Low frequency signals propagate through it. High frequencies are attenuated. This is caused by the frequency sensitivity of the capacitor.
The current through a capacitor is proportional to the time derivative of the voltage.
The phasor version of Equation 1 is,
(1)
Summing the phasor voltages around the loop in Figure 1 yields,
(2)
Solving for the current,
(3)
Using the current in Equation 4, we can find the voltage across the capacitor.
(4)
The magnitude of the voltage across the capacitor is,
(5)
The phase of V_{o} relative the voltage source, V is,
(6)
(7)
Equipment
Measure
Plot on the attached semi log paper,
(8)
Use the logarithmic axis for frequency.
FIVE  [Reflect] 
Reflect upon your observations.Q: Does the circuit pass low frequencies and attenuate high frequencies?
Q: Is the output inversely proportional to frequency at high frequencies as predicted by Equation 5?