• Support PF! Buy your school textbooks, materials and every day products Here!

Maximum energy stored in a capacitor? RLC circuit

  • Thread starter Luke Cohen
  • Start date
  • #1
30
1

Homework Statement


The current in a series RLC circuit leads the generator voltage by φ = 30°. The circuit, containing an inductor L = 400 mH and a resistor R = 50 Ω, is driven by a generator operating at ω = 100 rad/s with a maximum emf of 10 V. The capacitance is unknown.

The first question regarding this prompt is to find the capacitance, which is 145e-6F.

This is the question I am stumped on:

In terms of the maximum energy UC,max stored in the capacitor and the angle φ by which the current leads the generator voltage, the energy UC stored in the capacitor when the time is t = π/2ω is:

The correct answer is UC = UC,max sin^2φ

Homework Equations




The Attempt at a Solution


I've drawn my phasor diagrams, but I don't understand the correct answer. Is the voltage across the capacitor the component of the voltage across the generator pointing in the direction of X_c, the capacitor's impedance? If so, I get how a sin^2(phi) term would be used, because that would be the V^2 part of U = 1/2*cV^2, but I don't see how that would give me UC,max *sin^2(phi).
I will appreciate any help!


 

Answers and Replies

  • #2
30
1
This is just a normal box series RLC circuit with a battery, resistor, capacitor, and inductor in series. Sorry for not including!
 
  • #3
ehild
Homework Helper
15,409
1,813
Y

Homework Statement


The current in a series RLC circuit leads the generator voltage by φ = 30°. The circuit, containing an inductor L = 400 mH and a resistor R = 50 Ω, is driven by a generator operating at ω = 100 rad/s with a maximum emf of 10 V. The capacitance is unknown.

The first question regarding this prompt is to find the capacitance, which is 145e-6F.

This is the question I am stumped on:

In terms of the maximum energy UC,max stored in the capacitor and the angle φ by which the current leads the generator voltage, the energy UC stored in the capacitor when the time is t = π/2ω is:

The correct answer is UC = UC,max sin^2φ

Homework Equations




The Attempt at a Solution


I've drawn my phasor diagrams, but I don't understand the correct answer. Is the voltage across the capacitor the component of the voltage across the generator pointing in the direction of X_c, the capacitor's impedance? If so, I get how a sin^2(phi) term would be used, because that would be the V^2 part of U = 1/2*cV^2, but I don't see how that would give me UC,max *sin^2(phi).
I will appreciate any help!
You have to work with time dependence of the current and voltages. Assuming the generator voltage is Vg=Vg0sin(ωt),
what is the time dependence of the current and the capacitor voltage?
 
  • #4
NascentOxygen
Staff Emeritus
Science Advisor
9,244
1,070
This is just a normal box series RLC circuit with a battery, resistor, capacitor, and inductor in series. Sorry for not including!
There is no escaping this: you will need to show, and then use, the phasor diagram of current and voltages.
 

Related Threads for: Maximum energy stored in a capacitor? RLC circuit

Replies
6
Views
7K
  • Last Post
Replies
2
Views
10K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
554
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
805
  • Last Post
Replies
8
Views
2K
Top