# Energy in an RC Circuit?

• Jahosaphatz
In summary, the conversation discusses a problem involving an RC circuit with an EMF, resistor, and capacitor in series. The goal is to prove that the energy stored in the capacitor while charging is equal to half of the energy supplied by the EMF, and to show how much energy is lost by the resistor. The equations P = dW/dt and P = IV = I^2R = V^2/R are mentioned. The suggestion is to use power, dW/dt, and integrate indefinitely, incorporating the charging equation and using I = dQ/dt to calculate the current through the resistor.

## Homework Statement

I have an RC Circuit. There's the EMF (voltage supplier; battery), a resistor, and a capacitor. They are all in series. I need to prove that

--the energy stored in the capacitor through it charging equals 1/2 the energy supplied by the EMF

Then I need to show

--how much energy is lost by the resistor (which should be the other 1/2 of the energy supplied by the EMF by conservation of energy) and I need to prove it other than just using conservation of energy.

Since this problem is all ratios, you can use whatever variables you want (E, i, Q, V, etc) so long as they cancel

## Homework Equations

P = dW/dt

P = IV = I^2R = V^2/R

q = Q(1-e^(-t/(RC)))

There may be more I need.. I really don't know..

## The Attempt at a Solution

I'm thinking to use power, which is dW/dt, and integrate indefinitely. I don't know how to incorporate the charging equation, but I'm pretty sure its part of determining the energy of the capacitor?

You're on the right track. Use I = dQ/dt, calculate the current through the resistor, use this to calculate the power, and integrate.

## 1. What is an RC circuit?

An RC circuit is a circuit that contains both a resistor (R) and a capacitor (C). These components work together to control the flow of electricity and store energy.

## 2. How does an RC circuit store energy?

When a voltage is applied to an RC circuit, the capacitor charges up and stores energy. This energy is released when the capacitor discharges, creating a current in the circuit.

## 3. What is the time constant in an RC circuit?

The time constant in an RC circuit is a measure of how quickly the capacitor charges or discharges. It is calculated by multiplying the resistance (R) in ohms by the capacitance (C) in farads.

## 4. How does the resistance affect the behavior of an RC circuit?

The resistance in an RC circuit determines how quickly the capacitor charges and discharges. A higher resistance will result in a longer time constant and slower charging and discharging, while a lower resistance will result in a shorter time constant and faster charging and discharging.

## 5. What is the relationship between the capacitor and the voltage in an RC circuit?

The voltage across the capacitor in an RC circuit is directly proportional to the charge on the capacitor. As the capacitor charges, the voltage across it increases, and as it discharges, the voltage decreases.

• Introductory Physics Homework Help
Replies
2
Views
714
• Introductory Physics Homework Help
Replies
5
Views
5K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
969
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
22
Views
1K
• Introductory Physics Homework Help
Replies
19
Views
3K