Engineering Effective Voltage in series RLC circuit

[Pewgs]

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.

 

[rude man]

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.

 

[Pewgs]

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?

 

[rude man]

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.