RC circuit and discharging a capacitor

In summary, RC circuits can be used to discharge a capacitor by setting a function generator to produce a square wave with a peak voltage and period, and using the equation V(t) = Vo * e^(-t/RC) to graph the voltage across the capacitor over time. The amplitude of the square wave represents the initial voltage (Vo) and the frequency should be set to 2 Hz for the given circuit with RC = 0.183 seconds. The time/div should be set to 500 ms for best results.
  • #1
-EquinoX-
564
1

Homework Statement



RC circuits and discharging a capacitor

ok, say I have the following:

R = 4700 ohm
C = 39 micro farads
they are arranged in series and the battery is replaced using a function generator, which we set to produce a square wave (on/off). With any frequencies set.

How can I graph the Vcap vs time?

Homework Equations


The Attempt at a Solution



I know the equation V(t) = Vo * e^(-t/RC) can be used.. however in this case what is Vo (initial voltage) here?

if this is so then what is the purpose of the square wave function generator? Doesn't it matter on how big the frequencies are set?
 
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  • #2
Are the R and C in series or parallel? :smile:
 
  • #3
aniketp said:
Are the R and C in series or parallel? :smile:

oops forgot to mention that, it's in series
 
  • #4
If you are familiar with Laplace transformation, this problem can simply be solved by making a laplace transformation of the circuit and calculating the necessary value.
 
  • #5
no.. I am not familiar with Laplace transformation
 
  • #6
anyone?
 
  • #7
When you swith on the function generator, a peak voltage will be across RC circuit. During horizontal protion of the square wave, capacity will start charging. During vertically down ward portion and next horizontal portion of the square wave the capacity will discahrge.
 
  • #8
so I want to get this numerically... is there a way to compute it
 
  • #9
If you know the peak voltage and the period of the square wave, it is possible to find V(t).
 
  • #10
well the period of the square wave I know, but how do I get the peak voltage?

I am just using a normal function generator.. so maybe the peak voltage is known...
 
  • #11
You can select the peak voltage of the function generator, say 20 V peak-to-peak and period 500 ms. (greater then time constant RC). Find the voltage at every 50 ms. Plot the graph V(t) vs time.
 
  • #12
I don't want to do this experimentally.. I want to do this on paper actually... so if the peak voltage is 20V and period was 500 ms what is the Vo
 
  • #13
How can I graph the Vcap vs time?
To draw graph use V(t) = 20*e^-t/RC formula.
Put the values of t as 50ms. 100ms, ,,and so on. Substitute the values of RC. Find the values of V(t)
 
  • #14
ok.. gotcha.. is there actually a setting in the function generator to set the peak voltage... or is that hard coded in every function generator
 
  • #15
Yes. It is there. It can be varied, say from 0 to 30V.
 
  • #16
What does the amplitude take account for?
 
  • #17
-EquinoX- said:
What does the amplitude take account for?

Which amplitude? Amplitude of square wave it self is the Vo.
 
  • #18
What would be a good frequency to set on the function generator if the amplitude was around 2-5V and the RC is as I specified in my first post... I need some range of the frequency
 
  • #19
In the given circuit the time constant RC = 0.183 S. So to draw the graph, if possible set the function generator to 2 Hz.
 
  • #20
what is S there? 2 Hz.. isn't that really2 small? What should I set the time/div to be
 
  • #21
-EquinoX- said:
what is S there? 2 Hz.. isn't that really2 small? What should I set the time/div to be

Set to 500 ms.
 
  • #22
and what is S?
 
  • #23
RC is the time constant and it is measured in seconds.
 

FAQ: RC circuit and discharging a capacitor

How does an RC circuit work?

An RC (resistor-capacitor) circuit consists of a resistor and a capacitor connected in series or parallel. When the circuit is connected to a power source, the capacitor charges up to the same potential as the source. As the capacitor charges, the current flowing through the circuit decreases until it reaches zero, at which point the capacitor is fully charged. The capacitor then discharges through the resistor, creating a current in the opposite direction.

What is the purpose of a resistor in an RC circuit?

The resistor in an RC circuit serves to limit the current flow and control the rate of charging and discharging of the capacitor. It also helps to stabilize the circuit and prevent damage to the components. Without a resistor, the capacitor would charge and discharge too quickly, leading to potential circuit failure.

How does a capacitor discharge in an RC circuit?

When a capacitor is discharged in an RC circuit, the stored energy in the capacitor is released and flows through the circuit in the opposite direction. As the capacitor discharges, the voltage across it decreases, and the current flowing through the circuit increases until the capacitor is fully discharged, and the current returns to zero.

What is the time constant of an RC circuit?

The time constant of an RC circuit is a measure of how quickly the capacitor charges or discharges. It is determined by the product of the resistance and capacitance in the circuit. A larger time constant means a slower charging or discharging process, while a smaller time constant means a faster process.

How does the value of the resistor and capacitor affect the discharging time of a capacitor in an RC circuit?

The value of the resistor and capacitor in an RC circuit directly affects the discharging time of the capacitor. A larger resistor or capacitor will result in a longer discharging time, while a smaller resistor or capacitor will result in a shorter discharging time. This is because the time constant is directly proportional to the product of the resistance and capacitance, as mentioned in the previous question.

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