Energy dissipated in RC circuits

In summary, the conversation discusses the investigation of energy transfer in circuits with batteries, resistors, and a capacitor. The first step is to connect an uncharged capacitor in a simple series circuit with a resistor and a battery and wait for the circuit to reach a steady state. Then, the capacitor is disconnected and connected in a simple circuit with a resistor (of different resistance) only, waiting for a new steady state. The goal is to find algebraic expressions for the total energy dissipated by each resistor. The formula for the stored energy in a charged capacitor is also discussed, as well as the current during the capacitor's charging and discharging processes.
  • #1
meg29
1
0
1. You are investigating how energy is transferred in circuits with batteries, resistors, and a capacitor. First you take an uncharged capacitor and connect it in a simple series circuit with a resistor and a battery. You wait for the circuit to reach a steady state. After a steady state is reached, you disconnect the capacitor. You then connect the capacitor in a simple circuit with a resistor (of different resistance) only (no battery) and wait for this second circuit to reach a new steady state. Your job is to find algebraic expressions that represent the total energy dissipated by each resistor.


Homework Equations



t=0, deltaVc=0
t→∞ deltaVc=Vo
deltaV =Q/C ⇔Q=C*deltaVc=CVo
 
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  • #2
Do you know the formula for the stored energy in a charged capacitor? If not, can you derive it, using the voltage (=energy per new charge) as function of the charge at the capacitor?
 
  • #3
meg29 said:
1. You are investigating how energy is transferred in circuits with batteries, resistors, and a capacitor. First you take an uncharged capacitor and connect it in a simple series circuit with a resistor and a battery. You wait for the circuit to reach a steady state. After a steady state is reached, you disconnect the capacitor. You then connect the capacitor in a simple circuit with a resistor (of different resistance) only (no battery) and wait for this second circuit to reach a new steady state. Your job is to find algebraic expressions that represent the total energy dissipated by each resistor.


Homework Equations



t=0, deltaVc=0
t→∞ deltaVc=Vo
deltaV =Q/C ⇔Q=C*deltaVc=CVo


Total energy dissipated in each resistor is ∫i2R dt from 0 to ∞.

What is the current i(t) while the capacitor charges?

What is i(t) while the capacitor discharges?
 

FAQ: Energy dissipated in RC circuits

1. What is an RC circuit and how does it work?

An RC circuit is a simple circuit that consists of a resistor (R) and a capacitor (C) connected in series or parallel. When a voltage is applied to the circuit, the capacitor charges up to the same voltage as the source, while the resistor limits the flow of current. As the capacitor charges, the voltage across it increases until it reaches the same voltage as the source. Once the capacitor is fully charged, it stops the flow of current, and the voltage across it remains constant.

2. How does energy get dissipated in an RC circuit?

In an RC circuit, energy is dissipated through the resistor as heat. This is because the resistor limits the flow of current and converts electrical energy into heat energy. As the capacitor charges and discharges, the resistor experiences a constant flow of current, and heat is produced as a byproduct.

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

The amount of energy dissipated in an RC circuit depends on the capacitance of the capacitor, the resistance of the resistor, and the voltage applied to the circuit. A larger capacitor will store more energy, and a higher resistance will result in a larger voltage drop and therefore more energy dissipation. The voltage applied to the circuit also plays a significant role, as higher voltages will result in more energy being dissipated.

4. How does the time constant affect energy dissipation in an RC circuit?

The time constant, denoted by the symbol τ (tau), is a measure of how quickly the capacitor charges and discharges in an RC circuit. It is calculated by multiplying the resistance (R) and capacitance (C) values. A larger time constant means that the capacitor takes longer to charge and discharge, resulting in less energy dissipation. Conversely, a smaller time constant means that the capacitor charges and discharges more quickly, leading to more energy dissipation.

5. Can energy be recovered in an RC circuit?

In an ideal RC circuit, all the energy stored in the capacitor is dissipated through the resistor. However, in a real circuit, some energy may be lost due to factors such as resistance in the wires and internal resistance of the components. Therefore, it is not possible to recover all the energy in an RC circuit, but measures can be taken to minimize energy loss, such as using higher quality components with lower internal resistance.

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