# Energy dissipated in RC circuits

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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mfb
Mentor
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
Homework Helper
Gold Member
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?