# Effective Voltage in series RLC circuit

• Engineering
• 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

## 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.

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?

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.