Effective Voltage in series RLC circuit

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Discussion Overview

The discussion revolves around finding the effective voltage across each element in a series RLC circuit with a sinusoidal voltage input. Participants explore the relationships between voltage, current, impedance, and the phase angle in the context of circuit analysis.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents the initial conditions of the circuit, including the effective values of voltage and current, the phase difference, and the values of inductance and angular frequency.
  • Another participant questions the expression for the angle between current and applied voltage, emphasizing the importance of sign in determining whether current leads or lags voltage.
  • There is a suggestion that the equations will depend on the values of resistance (R), inductance (L), and capacitance (C), and that these values could be solved for based on the given information.
  • Participants discuss the significance of the effective voltage and current equations, and the concept of impedance in the circuit.
  • One participant asks about the relevance of the initial statement regarding effective values, indicating a need for clarification on its implications.

Areas of Agreement / Disagreement

Participants appear to agree on the need to derive expressions for voltage and current in relation to R, L, and C. However, there is uncertainty regarding the specific calculations and the significance of certain statements, indicating that the discussion remains unresolved.

Contextual Notes

The discussion lacks specific values for resistance and capacitance, which may limit the ability to fully solve the circuit equations. Additionally, the implications of the phase relationship between voltage and current are not fully explored.

Who May Find This Useful

This discussion may be useful for students studying circuit analysis, particularly those interested in RLC circuits and the concepts of effective voltage, impedance, and phase relationships in AC circuits.

Pewgs
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Homework Statement


Given a series RLC circuit with a sinusoidal voltage input, find the effective voltage across each element.

Given:

1) If the effective value of the source voltage is 1 V, the effective value of the current is 1 amp.
2) i(t) lags v(t) by 45 degrees
3) L=1H
4) w=2 rads/sec

Homework Equations


Veff = [1/T * ∫ v^2(t) dt] ^ (1/2)
Ieff = Im/√2
Veff = Vm/√2

The Attempt at a Solution


Based on the information I know that:
v(t) = Vmsin(2t)
i(t) = Imsin(2t-45)

Not exactly sure where to go from here especially since R and C aren't given, but I'm assuming you don't need these values or can find out based on the information already given.
 
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For an RLC series circuit, what is the expression for the angle between current i and applied voltage V? Be careful of sign (i leads vs. lags V).

For same circuit, what is the expression for the magnitude of impedance (V/i)?

2 equations, 2 unknowns, solve.
 
Ok I'm assuming each equation will be a function of R, L, and C? So I could solve for R and C?

From there do I just find the voltage/current as a function of time across each element and solve from there?

What is the significance of the first given statement?
 
Pewgs said:
Ok I'm assuming each equation will be a function of R, L, and C? So I could solve for R and C?

From there do I just find the voltage/current as a function of time across each element and solve from there?

Yes. Have you had complex impedances yet? Like Z = R + jwL stuff? Makes it rough if you haven't.

What is the significance of the first given statement?

|V/i| is one of your two equations. It's the magnitude of impedance of the circuit, i.e. without regard to the phase angle between V and i.
 

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