Capacitor - Resistor || Capacitor - Capacitor AC circuit

In summary, the charge on the right hand plate of the last capacitor in the AC circuit is described by the formula Q(t) = A.cos(wt), which can be derived by considering the total impedance and current in the circuit.
  • #1
Master J
226
0
An AC circuit consists of 3 segments: a capacitor, then another capacitor which is in parallel with a resistor, and then finally another capacitor, these 3 segments being in series with each other.

The formula which describes the charge Q(t) on the left hand side plate of the first capacitor is A.sin(wt). I need to find the formula which describes the charge on the right hand plate of the last capacitor (no.3).


Attempt:

I tried working in currents I. So the equation above becomes wAcos(wt). The total impedance Z of the 2nd segment is Z_1.Z_2 / Z_1 + Z_2, which is just R / ( 1 + RwC ).

I figured that the current at the last capacitor would be V / Z = I, where V is the potential. Since the current and voltage are out of phase by 90 degrees in the first capacitor, I got V = A.cos(wt).

So From this I get I, and just integrate to get Q(t). I don't think I am correct tho. I always have trouble with electrical circuits. Could someone perhaps point me in the right way?
 
Physics news on Phys.org
  • #2
Answer: The charge on the right hand plate of the last capacitor is given by Q(t) = A.cos(wt). This can be derived using the following steps:1. The total impedance of the second segment (which consists of a capacitor in parallel with a resistor) is given by Z = R/(1 + RwC), where R is the resistance, w is the angular frequency, and C is the capacitance. 2. The current flowing through the second segment is then I = V/Z = A.cos(wt)/R/(1 + RwC).3. Since the capacitors are in series, the current flowing through the third capacitor is the same as the current flowing through the second segment. 4. Thus, the charge on the right hand plate of the third capacitor is given by Q(t) = A.cos(wt).
 

1. What is a Capacitor - Resistor || Capacitor - Capacitor AC circuit?

A Capacitor - Resistor || Capacitor - Capacitor AC circuit is an electrical circuit that consists of capacitors and resistors connected in parallel or series, designed to allow the flow of alternating current (AC) while limiting the flow of direct current (DC).

2. How does a Capacitor - Resistor || Capacitor - Capacitor AC circuit work?

In this circuit, the resistors limit the amount of current that can flow through the circuit, while the capacitors store and release electrical energy as the AC current alternates. This allows the circuit to filter out unwanted frequencies and pass only desired frequencies.

3. What are the applications of a Capacitor - Resistor || Capacitor - Capacitor AC circuit?

These circuits are commonly used in electronic devices such as filters, amplifiers, and oscillators. They are also used in power supplies, audio equipment, and communication systems.

4. What are the advantages of using a Capacitor - Resistor || Capacitor - Capacitor AC circuit?

One major advantage of these circuits is their ability to filter out unwanted frequencies, making them useful in signal processing applications. They also have a compact design and can be easily integrated into electronic systems.

5. What are the limitations of a Capacitor - Resistor || Capacitor - Capacitor AC circuit?

One limitation is that the circuit may experience voltage drops due to the presence of resistors, which can affect the performance of the circuit. Additionally, these circuits may be sensitive to changes in temperature and can be affected by stray capacitance and inductance in the circuit.

Similar threads

  • Introductory Physics Homework Help
Replies
20
Views
206
  • Introductory Physics Homework Help
Replies
9
Views
134
  • Introductory Physics Homework Help
Replies
15
Views
896
  • Introductory Physics Homework Help
Replies
4
Views
647
  • Introductory Physics Homework Help
Replies
3
Views
654
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
20
Views
972
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
951
  • Introductory Physics Homework Help
Replies
9
Views
2K
Back
Top