Help with Circuits Capacitance & Inductance

In summary, In the first two equations of the opamp problem, shouldn't the Vp be Vn instead?; If not is there another way of solving this equation.
  • #1
deyiengs
5
0
The images tell it all. Please help someone.


http://image.cramster.com/answer-board/image/200941884006337564080009162509346.jpg


on this diagram, the expression IL(t) should read I(t).

http://image.cramster.com/answer-board/image/2009418845296337564112974787505740.jpg
 
Last edited by a moderator:
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  • #2
Welcome to PF!

Hi deyiengs! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
Thanks Tiny-tim for taking your time. I planned to post what i had but i forgot.
On the first one, how do you get R- thevinin? If that's the way to go about it?.
On the second one I need the initial and final conditions. I used -5mA and did a source transformation to get -2.1mA as the initial consition. I used 5mA for final and got 2.1mA as the final conditio for the inductor. Then used the formula:
iL = (i(initial) - i(final))e^(-1/tc)+ i(final)
My tc was 3.3333us
Then used VL = L di/dt

Is that close to the correct way or did I deviate
 
  • #4
On the following diagram, I have the following for finding Vo:

node analysis on the top nope of the Vn
http://image.cramster.com/answer-board/image/cramster-equation-2009419162557633757551572010000561.gif
This would lead to
http://image.cramster.com/answer-board/image/cramster-equation-20094191627356337575525582600002527.gif

but i need to replace Vp by Vs.

Hence for the node on the bottom part I have:
http://image.cramster.com/answer-board/image/cramster-equation-200941916329633757555299510000920.gif
I'm stuck here how can I factor out Vp on the above equation. is it possible if it it how.

http://image.cramster.com/answer-board/image/2009419162211633757549313416250747.jpg

If not is there another way of solving this equation.
 
Last edited by a moderator:
  • #5
In the first two equations of the opamp problem, shouldn't the Vp be Vn instead?
 
  • #6
The Electrician said:
In the first two equations of the opamp problem, shouldn't the Vp be Vn instead?

yes but Vp = Vn
 
  • #7
Someday you may have to find a transfer function where the opamp isn't ideal. In that case, Vp#Vn, so it's good practice to use the symbol for the actual node that you're writing an equation for. Then at the end, if the opamp is ideal, substitute Vp=Vn. This way, you avoid mistakes in setting up your equations.
 
  • #8
The Electrician, could you help me solve it if you can please
 
  • #9
You can either solve your two simultaneous differential equations, or you can solve it in the Laplace domain. I would do the latter. Have you studied the use of the s-variable for solving AC circuits?

Set up two equations:

s*C*Vn + (1/R)*(Vn-Vs) = 0

s*C*(Vp-Vs) + Vp/R = 0

Now, you also know that Vp = R/(R + 1/(s*C)) * Vs by the voltage divider rule, and Vp=Vn.

Substitute that that last equation, Vp = R/(R + 1/(s*C))*Vs, for both Vp and Vn in the first two equations. Then you will have two simultaneous equations you can solve with simple algebra.

The solution is Vo = s*R*C*Vs, which in the time domain is Vo = R C d/dt(Vs). This ignores initial values for charge on C.
 

1. What is capacitance and how does it affect circuits?

Capacitance is the ability of a circuit element to store electric charge. It is measured in farads and is represented by the letter C. Capacitance affects circuits by storing energy in an electric field, which can be used to smooth out fluctuations in voltage and filter out unwanted frequencies.

2. How do capacitors and inductors differ in their function within a circuit?

Capacitors store electric charge and release it as needed, while inductors store energy in a magnetic field and release it as a magnetic field collapses. Capacitors are used to block DC signals and allow AC signals to pass through, whereas inductors are used to block AC signals and allow DC signals to pass through.

3. What is the relationship between capacitance and voltage?

The relationship between capacitance and voltage is directly proportional. This means that as capacitance increases, so does voltage, and vice versa. This can be represented by the equation C=Q/V, where C is capacitance, Q is electric charge, and V is voltage.

4. How do you calculate the total capacitance of a series or parallel circuit?

In a series circuit, the total capacitance is equal to the inverse of the sum of the inverses of individual capacitances. In a parallel circuit, the total capacitance is equal to the sum of individual capacitances. These can be represented by the equations 1/Ctotal = 1/C1 + 1/C2 + ... and Ctotal = C1 + C2 + ..., respectively.

5. What is the role of capacitance and inductance in resonance?

Capacitance and inductance work together to create resonance in circuits. When the capacitance and inductance values are just right, the circuit will vibrate at its natural frequency, amplifying the input signal. This is useful in many electronic devices, such as radios, where resonance is used to select specific frequencies.

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