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Effective Voltage in series RLC circuit

  • Engineering
  • Thread starter Pewgs
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
rude man
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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.
 
  • #3
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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?
 
  • #4
rude man
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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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