RC circuit where source depends on capacitor current

In summary, the conversation mainly focused on solving a circuit problem using KVL and substitution methods. There were discussions about finding the value of Io and Q, and understanding the behavior of capacitors and controlled sources in circuits. The main takeaway was to pay attention to sign conventions and understand the equivalent component of a controlled source. There were also clarifications made about the initial conditions of the circuit.
  • #1
miyelmunshi
10
0
Homework Statement
Find Io(t) for t>0 of the circuit shown
Relevant Equations
I(t) = C x dv/dt
V = Q/C
271390334_717245076330411_2590546543826551150_n.png

I did a kvl loop and got V + 5Io - 15 Io = 0
So, V = 10Io
Then, substituted dq/dt for Io and q/c for V
I get to dq/dt - 50000q = 0
solving this equation i get q = C x e^50000q (c for constant)

my Io = dq/dt
so Io now is 50,000Ce^50000q

now my Q(0) is 3 x 10^-5
So my Io (0) should be, 50,000Ce^1.5

.
I don't know how to find the C now or any of the things i did is even correct

I know the answer should be
15e^-25000t for V(t)
0.75e^-25000t for Io(t)
 
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  • #2
miyelmunshi said:
I don't know how to find the C
See the diagram carefully?
 
  • #3
cnh1995 said:
See the diagram carefully?
Ummm can not figure out anything unfortunately :)
 
  • #4
cnh1995 said:
See the diagram carefully?
are rest of my process correct ?
 
  • #5
cnh1995 said:
See the diagram carefully?
Ok i looked at it again so i can i do a kvl loop for Io(0) and put the voltage of capacitor as 15 v ? then get the value of Io(0) ?
 
  • #6
It might be useful to note that the control law for the controlled source is 5*Io and ask yourself what kind of electronic component has the property that the voltage across it is proportional to the current through it. In other words, what standard passive component is the controlled source equivalent to?
 
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  • #7
The Electrician said:
It might be useful to note that the control law for the controlled source is 5*Io and ask yourself what kind of electronic component has the property that the voltage across it is proportional to the current through it. In other words, what standard passive component is the controlled source equivalent to?
a resistor maybe ? but why is that important ?
 
  • #8
You made a sign mistake in your the KVL equation in your original post.

You need to be a little more precise about ##i_0##. ##i_0(0)## is ambiguous because there's a discontinuity at ##t=0## in ##i_0##. Can you tell us what ##i_0(0^-)## is, assuming the switch has been in position 1 for a long time?
 
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  • #9
vela said:
You made a sign mistake in your the KVL equation in your original post.

You need to be a little more precise about ##i_0##. ##i_0(0)## is ambiguous because there's a discontinuity at ##t=0## in ##i_0##. Can you tell us what ##i_0(0^-)## is, assuming the switch has been in position 1 for a long time?
in position 1 as far as i know, no current flows through the circuit as there is no voltage difference, so shouldn't Io be 0 then ? for t < 0 ?
 
  • #10
Right. The capacitor acts like an open circuit after it's charged, so ##i_0(0^-)=0## and ##V(0^-)=15~\rm V##.

Instead of focusing on ##i_0##, consider ##Q## for ##t>0##. Recall that the voltage across a capacitor is continuous, so you know that ##V(0^+) = V(0^-) = 15~\rm V##. What does this mean about ##Q(0^+)##?
 
  • #11
vela said:
Right. The capacitor acts like an open circuit after it's charged, so ##i_0(0^-)=0## and ##V(0^-)=15~\rm V##.

Instead of focusing on ##i_0##, consider ##Q## for ##t>0##. Recall that the voltage across a capacitor is continuous, so you know that ##V(0^+) = V(0^-) = 15~\rm V##. What does this mean about ##Q(0^+)##?
i don't really understand what you are getting into but q should be CV so, 3x10^-5 maybe ?
 
  • #12
miyelmunshi said:
i don't really understand what you are getting into.
Like what part?

miyelmunshi said:
but q should be CV so, 3x10^-5 maybe ?
Right, other than the lack of units. So you essentially have an expression for ##q(t)## for ##t>0##, right? From that, you can find the results you want (after you fix the sign mistake).
 
  • #13
vela said:
Like what part?Right, other than the lack of units. So you essentially have an expression for ##q(t)## for ##t>0##, right? From that, you can find the results you want (after you fix the sign mistake).
um if i fix the sign mistake will the equation be V + 20 Io?
 
  • #14
miyelmunshi said:
um if i fix the sign mistake will the equation be V + 20 Io?
That's ,not an equation.

Perhaps you mean that ## V = 20 I_0 ## .
 
  • #15
miyelmunshi said:
a resistor maybe ? but why is that important ?
If the controlled source were replaced with a 5 ohm resistor, would the signs in your equation be any different?
 
  • #16
The Electrician said:
If the controlled source were replaced with a 5 ohm resistor, would the signs in your equation be any different?
i don't think so
 
  • #17
SammyS said:
That's ,not an equation.

Perhaps you mean that ## V = 20 I_0 ## .
I meant v+20Io = 0
 

Related to RC circuit where source depends on capacitor current

1. What is an RC circuit where the source depends on capacitor current?

An RC circuit is a type of electrical circuit that contains a resistor (R) and a capacitor (C). In this specific type of RC circuit, the source of the circuit is dependent on the current flowing through the capacitor. This means that the voltage of the source will change depending on the amount of current stored in the capacitor.

2. How does the source voltage change in an RC circuit where the source depends on capacitor current?

The source voltage in this type of RC circuit will change as the capacitor charges and discharges. When the capacitor is fully charged, the source voltage will be at its maximum. As the capacitor discharges, the source voltage will decrease until the capacitor is fully discharged and the source voltage returns to its original value.

3. What is the purpose of using an RC circuit where the source depends on capacitor current?

This type of RC circuit is commonly used in electronic devices to control the timing and frequency of signals. By varying the amount of current flowing through the capacitor, the source voltage can be manipulated to create different waveforms and frequencies.

4. How does the time constant affect an RC circuit where the source depends on capacitor current?

The time constant, which is the product of the resistance and capacitance in the circuit, determines the rate at which the capacitor charges and discharges. A larger time constant will result in a slower rate of change in the source voltage, while a smaller time constant will result in a faster rate of change.

5. What are the advantages and disadvantages of using an RC circuit where the source depends on capacitor current?

The advantages of using this type of RC circuit include its simplicity, low cost, and ability to generate a wide range of waveforms and frequencies. However, it can be sensitive to changes in temperature and can have a limited frequency range. Additionally, the source voltage may not be constant, which can affect the performance of some electronic devices.

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