Energy dissipated in RC circuits

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SUMMARY

The discussion focuses on the energy transfer in RC circuits involving a capacitor, resistor, and battery. It details the process of charging an uncharged capacitor in a series circuit until a steady state is reached, followed by discharging the capacitor through a resistor without a battery. The total energy dissipated in each resistor is expressed as the integral of the current squared times the resistance, specifically ∫i²R dt from 0 to ∞. Key equations include deltaV = Q/C and Q = C*deltaVc, which are essential for deriving the energy stored in the capacitor.

PREREQUISITES
  • Understanding of RC circuit theory
  • Familiarity with calculus, specifically integration
  • Knowledge of capacitor charging and discharging processes
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the derivation of the energy stored in a capacitor using the formula U = 1/2 C V²
  • Learn about the time constant in RC circuits and its impact on charging and discharging
  • Explore the concept of current i(t) during capacitor charging and discharging phases
  • Investigate the effects of varying resistance on energy dissipation in RC circuits
USEFUL FOR

Electrical engineering students, physics enthusiasts, and anyone studying circuit analysis or energy transfer in electrical systems will benefit from this discussion.

meg29
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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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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?
 
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?
 

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