# Solve AC Voltage Form: RLC Series Circuit Power

• Acuben
In summary, an AC voltage of the form V= (100 v) sin (1 000t) is applied to a series RLC circuit, where V is the peak voltage and ω is the angular frequency. The voltage at any instant T is V sin (ωT). The voltage can range from plus 100 volts to minus 100 volts, including zero. To find ω, compare the terms in the equation V=V0sin(ωt). The angular velocity is also related to frequency, where ω = 2πf.
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?

-----
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
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

Last edited:
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.

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

rock.freak667 said:
...
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 said:
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

.

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.

## 1. What is an RLC series circuit?

An RLC series circuit is a type of electrical circuit that consists of a resistor (R), inductor (L), and capacitor (C) connected in a series configuration. This means that the components are connected end-to-end, so that the same current flows through each component.

## 2. How do you solve for AC voltage in an RLC series circuit?

To solve for AC voltage in an RLC series circuit, you can use the formula V = IZ, where V is the voltage, I is the current, and Z is the impedance. The impedance can be calculated using the formula Z = √(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

## 3. What is the power in an RLC series circuit?

The power in an RLC series circuit is the rate at which energy is transferred or used. It can be calculated using the formula P = VI, where P is the power, V is the voltage, and I is the current. In an AC circuit, the power is given by the formula P = VrmsIrmscosφ, where Vrms and Irms are the root mean square values of the voltage and current, and φ is the phase angle between them.

## 4. How does changing the value of the components affect the AC voltage in an RLC series circuit?

Changing the value of a component in an RLC series circuit can affect the AC voltage in different ways. For example, increasing the resistance will decrease the voltage, while increasing the inductance or capacitance will increase the voltage. The exact effect will depend on the specific values of the components and the frequency of the AC source.

## 5. What are some real-world applications of RLC series circuits?

RLC series circuits have many real-world applications, including in electrical filters, resonance circuits, and power supplies. They are also commonly used in electronic devices such as radios, televisions, and computers. In power systems, RLC series circuits are used for power factor correction and voltage regulation.

Replies
8
Views
723
Replies
3
Views
575
Replies
15
Views
4K
Replies
9
Views
9K
Replies
2
Views
2K
Replies
2
Views
2K
Replies
2
Views
4K
Replies
5
Views
2K
Replies
8
Views
1K
Replies
5
Views
2K