Problems with First order RC circuit

In summary, the conversation is discussing a parallel RC circuit with a power source and switch. Part (a) asks for the voltage across the capacitor after the switch is closed at t=0. Part (b) asks for the voltage across the capacitor after the switch has been closed for a long time and then opened at t=0. The speaker asks for clarification on the method for solving part (a) and the physical implications for part (b). They also inquire about the respondent's knowledge of series RC circuits and Thevenin's theorem.
  • #1
thuc
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Member warned to use the homework template for posts in the homework sections of PF.
I have problems with question b. I don't know where to start. If the switch is on steady state, the current through capacitor would be 0 and i can't have K. This makes me confused.
This is the Total response function of a): V0(t) = K^(-1/2t)
 

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  • #2
The image shows a 12V power source with 2##\Omega## internal resistance connected, in parallel, with a parallel RC circuit (3F and 4##\Omega##) via a switch.
The voltage across the capacitor is labelled ##v_0##.
Part (a) says the switch, open for a long time, is closed at t=0, find ##v_0(t)##.
Part (b) says the switch has been closed for a long time, and is opened at t=0, find ##v_0(t)##.
These two parts normally have a similar method of solution, so please show your method for part (a) so we can see how you are thinking.

For part (b) ... what is physically happening? What is the initial voltage on the capactor, what happens to the charge on the capacitor for t>0?
 
  • #3
Ok, this is part a)
 

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  • #4
thuc said:
Ok, this is part a)
Are you familiar with the response of a series RC circuit excited with a step input?
Are you familiar with the Thevenin's theorem?
 

1. What is a first order RC circuit?

A first order RC circuit is a simple circuit that consists of a resistor (R) and a capacitor (C) connected in series. The capacitor is charged by a voltage source through the resistor, and the capacitor's charging and discharging behavior is controlled by the values of R and C.

2. What are the common problems with first order RC circuits?

The most common problems with first order RC circuits include time constant errors, voltage drops, and non-ideal behavior of the components. These issues can affect the accuracy and stability of the circuit's output.

3. How do time constant errors affect first order RC circuits?

Time constant errors occur when the time constant (RC) of the circuit is not properly matched to the input signal frequency. This can result in incorrect charging or discharging of the capacitor, leading to errors in the output voltage.

4. What causes voltage drops in first order RC circuits?

Voltage drops in first order RC circuits can be caused by the internal resistance of the voltage source, as well as the resistance of the components. These voltage drops can affect the overall voltage and current in the circuit, leading to errors in the output.

5. How can the non-ideal behavior of components affect first order RC circuits?

The components in a first order RC circuit, such as the capacitor and resistor, may not behave exactly as their ideal models predict. This can be due to factors like parasitic capacitance, leakage current, and tolerance values. These non-ideal behaviors can introduce errors in the circuit's output and affect its performance.

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