Question

In a lab quiz, you are given a resistor and a fully charged capacitor. You use Capstone to measure the capacitor's voltage while discharging it through the resistor and find that the capacitor's voltage decays to half its initial value in 2.25 ms.

(A) What is the time constant from the exponential decay? _________ ms

(B) You then connect the resistor and capacitor to an AC generator to make a low-pass filter. What is the crossover frequency in Hz? _____________Hz

Answer 1

The decay of voltage in the capacitor is given by
  
where, \tau is the time constant. So, if at time t, V(t) =(V_0)/2, then, we get
  
  
  
  
Now as t = 2.25 ms, so, the time constant is
   
  

B)

The crossover frequency of the low pass filter is the break frequency or the turnover frequency which is determined in terms of the time constant of the corresponding RC circuit and is given by
  
And so, for the above time constnant, \tau = 3.246 ms, we get the crossover frequency