Solve AC Voltage Form: RLC Series Circuit Power

[Acuben]

Homework Statement

You don't even have to read the whole thing... just the red part is sufficient.
I saw this on the homework: V= (100 v) sin (1 000t)
What does this mean?

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Can I treat it as having 100 real magnitude and 0 imaginary magnitude (and therefore 0 phase angle)? or does sin(1 000t) tells something about the phase angle?
or does sin (1 000t) tells something about angular velocity or frequency?

I can't solve this problem without knowing frequency or angular velocity

just for side note: let...
V= delta voltage
v= unit volts
uF= micro farad
H= Henries

RLC= i believe it stands for Resistance, Inductor, Capacitor
An AC voltage of the form V= (100 v) sin (1 000t) is applied to a series RLC circuit. Assume the resistance is 400 Ohms, the capacitance is 5.00 uF, and the inductance is 0.500 H. Find the average power delivered to the circuit

Homework Equations

w= angular velocity (supposed to be omega)
L= inductor
C= capacitor
j= complex coefficent = sqrt(-1)
Zl= resistance of inductor
Zc= resistance of capacitor
Ztot= total resistance
R= resistance of resistor
P= Power

Xl=wL
Xc=1/wc
Zl=j*Xl
Zc=-j*Xc
Ztot= R + Zl + Zc = R + j(Xl-Xc)

P=I*V*(P.F)

P.F= Power Factor. Is is cos $$\varphi$$
the angle between voltage and current.

by default everything is in RMS (rootmeansquare), but it shouldn't matter in calculation)

The Attempt at a Solution

well it's easy except I don't know frequency nor angular velocity.
Otherwise finding Ztot will be easy and finding power is easy as well

 

[rock.freak667]

Your voltage is V= (100 v) sin (1 000t), which is in the form V=V₀sin(ωt).

hence the amplitude is V₀ and the angular frequency is ω. Compare the terms and get ω.

 

[vk6kro]

The voltage at any instant T is V sin (wT) where w is (should be) omega, the angular velocity.

So, V is the peak voltage.

Omega = 2 * PI * F

In this case, omega = 1000 = 2 * PI * F ... so F = 159.154 Hz. ( ie 1000 / (2 * pi) )

V is the maximum voltage, but the actual voltage depends on the sine function, so the actual voltage can be anywhere between plus 100 volts and minus 100 volts, including zero.

For example what would the voltage be after 0.2 seconds?
V = 100 * sin (2 * pi * 159.154 * 0.2 ) or -34.2 volts

 

[Acuben]

...
which is in the form V=V₀sin(ωt).
...
hence the amplitude is V₀ and the angular frequency is ω. Compare the terms and get ω.

The voltage at any instant T is V sin (wT) where w is (should be) omega, the angular velocity.

So, V is the peak voltage.

V is the maximum voltage,

Thank you very much. I understood it now =D

 

[rwisz]

.

To solve this problem, we first need to find the impedance (Ztot) of the series RLC circuit. This can be done using the formula Ztot = R + j(Xl-Xc), where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance.

To find Xl and Xc, we use the formulas Xl = wL and Xc = 1/wC, where w is the angular velocity and L and C are the inductance and capacitance of the circuit, respectively.

However, since the frequency (f) is not given, we cannot directly calculate the angular velocity using the formula w = 2πf. Instead, we can use the given AC voltage form V = (100 v) sin (1 000t) to find the frequency.

In this equation, 100 v is the maximum voltage (amplitude), and 1 000t represents the angular velocity (2πf) multiplied by time. Therefore, we can rearrange the equation to find the frequency: f = 1 000t / 2π.

Substituting this value of frequency into the formula for angular velocity, we can now calculate the impedance Ztot and then find the average power delivered to the circuit using the formula P = I*V*(P.F).

In conclusion, the given AC voltage form provides information about the amplitude, frequency, and angular velocity of the circuit, which are all necessary to solve the problem and find the average power delivered to the circuit.