Energy dissipated in the resistors in a 2 mesh RC circuit

In summary: Although I have no idea of how to proceed, I did calculate the currents and voltages for each part of the circuit. Below are the results:For the switch:I find the current passing by the amperemeter (IA) and the voltage across the voltmeter VV after a long time t (t>5 time constants). The current is I find the voltage across the voltmeter VV passed 10 milliseconds. The voltage is For the resistor:The energy dissipated in the resistor until an instant t is The energy dissipated in the resistor until an instant t is The energy dissipated in the resistor until an instant t is For
  • #1
Eduardo Leon
6
0

Homework Statement


Hi mates, I have problems solving the third part of this exercise, I've already done all the previous calculations.

Given the following circuit, where the switch S is open, the power supply = 50 volts and:
  • The initial charge in the C capacitor: QC = 0 coulombs
  • The initial charge in the 2C capacitor: Q2C = 20^-6 coulombs
Calculate (with real instruments):
  1. Switch⇒I find the current passing by the amperemeter (IA) and the voltage across the voltmeter VV After a long time t (t>5 time constants). (Done).
  2. Switch⇒II find the voltage across the voltmeter VV passed 10 milliseconds. (Done).
  3. Switch⇒III next get the final reading of the voltmeter VV at a given time t (t >0 ∧ t< 5 time constants) and the energy dissipated in the resistors till that instant.
attachment.jpg

Homework Equations


  • Ohm's law: R=ΔV/i
  • Capacitance: C=q/ΔV
  • Kirchoff's laws: Σi=0 ∧ ΣΔV=0
  • Energy gived by the battery until an instant t
    Image1.gif
  • Energy dissipated in the resistor until an instant t
    Image2.gif
  • Energy stored in the capacitor until an instant t
    Image3.gif

The Attempt at a Solution


As stated before, I've done the first and the second parts.

For the first:
  • 58_59e4a5e4c7a317067e0e748d4c7303e8.png
    Amps*
  • 55_39ed5ab39f3e1b932d58b8143acf9655.png
    Volts*
For the second:
  • 49_549e15a8fc3c64f775b461c0ce4c83f2.png
    73_a3a7a2e80e63986351b15fb412bb6203.png
    34_76bab7f98db551c5bfbe82b73004a907.png
    Volts*
For the third:
Well, here is where i get lost, because I dont't know how to study and analize the circuit formed at this point, I've only seen discharging RC circuits whis a single current, one resistor and one capacitor due those elements could be joined into their equivalent ones, but here, I get 2 resistors, 2 capacitors and 2 meshes, like this one.

14v5xa2k62r2x


I know that the initial charges at this point are:

In order to get the initial charge in the C capacitor I used the voltage obtained in the voltmeter in the second part at the 10 milliseconds, because are connected parallel. So, multiplying that voltage times the capacitance, we get
49_f93ffa7bf895f1ac07d8dc5df756a1e0.png
The initial charge in the 2C capacitor stills equal, since its an ideal capacitor, so is the same: Q2C = 20^-6 coulombs
 

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  • #2
It would help things if you first produced a clearer circuit diagram.
 

Related to Energy dissipated in the resistors in a 2 mesh RC circuit

What is an RC circuit?

An RC circuit is an electrical circuit that contains both a resistor (R) and a capacitor (C). It is commonly used in electronic devices to control the flow of electricity and store energy.

What is energy dissipation?

Energy dissipation is the process by which energy is converted into heat and lost from a system. In the context of an RC circuit, it refers to the energy that is lost as heat in the resistors.

How is energy dissipated in a 2 mesh RC circuit?

In a 2 mesh RC circuit, energy is dissipated in the resistors due to the flow of current through them. As the current passes through the resistors, it encounters resistance, which causes the electrical energy to be converted into heat energy.

What factors affect the amount of energy dissipated in an RC circuit?

The amount of energy dissipated in an RC circuit is affected by the resistance of the resistors, the capacitance of the capacitor, and the voltage applied to the circuit. The higher the resistance and voltage, and the lower the capacitance, the more energy will be dissipated in the resistors.

How can energy dissipation be minimized in an RC circuit?

To minimize energy dissipation in an RC circuit, the resistance of the resistors can be reduced, the capacitance of the capacitor can be increased, and the voltage applied to the circuit can be lowered. Additionally, using more efficient resistors and capacitors can also help reduce energy dissipation.

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