Energy dissipated in RC circuits

[meg29]

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

 

[mfb]

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?

 

[rude man]

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?