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.

 

[DeeNos]

The effective voltage in a series RLC circuit can be calculated using the formula Veff = [1/T * ∫ v^2(t) dt] ^ (1/2), where T is the period of the sinusoidal voltage input. In this case, since the voltage input is sinusoidal, we can use the effective value of the source voltage (1 V) to calculate the effective value of the voltage across each element.

Using the given information, we can also determine that the effective value of the current is 1 amp, and that it lags the voltage by 45 degrees. This means that the current is also sinusoidal with an amplitude of 1 amp and a phase shift of -45 degrees.

Since the inductance (L) and angular frequency (w) are also given, we can use these values to calculate the impedance (Z) of the circuit, which is given by Z = √(R^2 + (wL)^2).

Finally, using the relationship between voltage, current, and impedance in a series circuit (V = IZ), we can find the effective voltage across each element by multiplying the effective current (1 amp) by the impedance of each element.

In summary, the effective voltage across each element in the series RLC circuit can be calculated as follows:

Veff = Ieff * Z
= (1 amp) * √(R^2 + (wL)^2)
= √(R^2 + (2L)^2)

Therefore, to find the effective voltage across each element, we need to know the value of R, which is not given in the problem. However, we can still determine the relationship between the effective voltages across each element by using the above formula.