Confused on the power through a Capacitor formula help

Click For Summary

Homework Help Overview

The discussion revolves around understanding the power through a capacitor and its relationship with energy stored in the capacitor, specifically focusing on the formula for power as a derivative of energy. The original poster expresses confusion regarding the application of these concepts in a circuit involving a switch and equivalent capacitance.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants explore the relationship between energy stored in a capacitor and power, questioning how to differentiate energy when it is treated as a constant. There are inquiries about finding expressions for potential and stored energy with respect to time, as well as the correct interpretation of capacitance and charge.

Discussion Status

The discussion is ongoing, with participants providing guidance on finding expressions related to potential and energy. There is an exploration of the correct formulas and the need for differentiable expressions, indicating a productive direction in clarifying misunderstandings.

Contextual Notes

Participants note the presence of a switch in the circuit that closes at t = 0, which may influence the behavior of the circuit and the calculations involved. There is also a mention of the need for an expression involving an exponential function related to the time constant.

nchin
Messages
172
Reaction score
0
I know that the energy stored in a capacitor is U = 1/2 CV2. but the power through it? I have in my notes that the power is the derivative of U.

so for example the energy is 26 Joules so the derivative of 26 J? doesn't make sense cause 26 is a constant.

help please!

i attached a picture of the problem. i first find the C equivalent.

oops! there's actually a switch on the top of the circuit! which closes at t = 0
 

Attachments

  • captors.PNG
    captors.PNG
    3.1 KB · Views: 561
Last edited:
Physics news on Phys.org
Can you find an expression for the potential across the equivalent capacitance with respect to time? How about the stored energy? This expression should be differentiable w.r.t. time...
 
gneill said:
Can you find an expression for the potential across the equivalent capacitance with respect to time? How about the stored energy? This expression should be differentiable w.r.t. time...

potential across is C = QV --> V(t) = C/Q(t). is that it?
 
nchin said:
potential across is C = QV --> V(t) = C/Q(t). is that it?

No. C is capacitance, not potential. C = QV is not a correct formula. And Q(t) does not provide any information about how the charge Q changes over time.

What is the expression for the voltage across the capacitance with respect to time for the given circuit? Hint: it involves an exponential function with a time constant.
 
Last edited:

Similar threads

I am building a power-bank for a project, out of capacitors
  • · Replies 14 ·
Replies
14
Views
2K
Determining Inductance L in an LC Circuit
  • · Replies 5 ·
Replies
5
Views
2K
Analysing a double capacitor circuit with no battery
  • · Replies 14 ·
Replies
14
Views
3K
Capacitor Questions Charging and Discharging
  • · Replies 4 ·
Replies
4
Views
4K
Calculating Energy Stored and Dissipated in a Capacitor Discharge
  • · Replies 1 ·
Replies
1
Views
2K
A circuit with switches, capacitators and resistors
  • · Replies 6 ·
Replies
6
Views
3K
RC Circuit with parallel resistor
  • · Replies 6 ·
Replies
6
Views
3K
Energy and Voltage of Capacitor Circuits
  • · Replies 5 ·
Replies
5
Views
1K
Lens Maker's Formula - Confusion in the derivation
  • · Replies 15 ·
Replies
15
Views
2K
Energy in capacitor at steady state
  • · Replies 10 ·
Replies
10
Views
2K