How do I determine the current amplitude and phase angle in an RLC AC circuit?

In summary, the voltage V(t)=V1 Re{eiwt} produces a current I(t)=I1 Re{e(iwt+θ). To determine I1 and θ, you need to find the complex impedance of the circuit, which can be written in exponential form as Z=|Z|eiψ. Then, using the equation I=V/Z, you can find the complex current I0= V0/|Z|ei(ωt+θ). To ensure that the magnitudes and phases are the same on both sides, the amplitudes used for I and V must be the same, represented by I1 and V1 in the original post.
  • #1
kate12
6
0
Voltage V(t)=V1 Re{eiwt} produces a current I(t)=I1 Re{e(iwt+θ). Determine I1 and θ.

The circuit is AC so do I treat it the same as an SHM question? Is π/2? And what do I need to do to find I1? I don't know where to start.
 
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  • #2
What is the circuit? You need its complex impedance to find I1 and θ.

ehild
 
  • #3
Ohh. The circuit is like this one:

pic012.png


with no values given.
 
  • #4
What is the impedance in terms of R, L, and C?

ehild
 
  • #5
z = R + iωL +1/iωC ?

ehild said:
What is the impedance in terms of R, L, and C?

ehild
 
Last edited:
  • #6
OK, collecting the imaginary terms, it is Z=R+i(ωL -1/ωC ). This is a complex number. You can write it in exponential form:

Z=|Z|e (How?).

The complex voltage is V=V1eiωt

Use the equation I=V/Z to find the complex current.

ehild
 
Last edited:
  • #7
ehild said:
OK, collecting the imaginary terms, it is Z=R+i(ωL -1/ωC ). This is a complex number. You can write it in exponential form:

Z=|Z|eiωt (How?).

The complex voltage is V=V1eiωt

Use the equation I=V/Z to find the complex current.

ehild
I=V0/|Z| ?

But that gives me I0= V0/|Z|ei(ωt+θ).
 
Last edited:
  • #8
kate12 said:
I=V0/|Z| ?

But that gives me I0= V0/|Z|ei(ωt+θ).

You used I1 and V1 for the amplitudes in the original post.

I=V/Z . Z=|Z|e

That means

I0ei(ωt+θ)=V0ei(ωt)/[|Z|e]

Simplify with ei(ωt).

I0e=V0/[|Z|e]=[V0/|Z|]e-iψ

The magnitudes and phases have to be the same on both sides.

ehild
 

1. What is an RLC AC circuit?

An RLC AC circuit is a type of electrical circuit that comprises of three main components: a resistor (R), an inductor (L), and a capacitor (C). These components are connected in series or parallel to form a circuit that can conduct alternating current (AC) electricity.

2. What is the purpose of an RLC AC circuit?

The purpose of an RLC AC circuit is to regulate the flow of AC electricity and to filter out certain frequencies. The resistor, inductor, and capacitor work together to control the amount of current and voltage in the circuit, making it useful for a variety of applications such as in filters, amplifiers, and oscillators.

3. How does an RLC AC circuit differ from a simple AC circuit?

An RLC AC circuit differs from a simple AC circuit in that it contains additional components, namely the inductor and capacitor. These components introduce reactance, which is the opposition to the flow of current, and this can affect the behavior of the circuit. In a simple AC circuit, only a resistor is present, which does not introduce reactance.

4. What is the resonance frequency of an RLC AC circuit?

The resonance frequency of an RLC AC circuit is the frequency at which the inductive reactance and capacitive reactance cancel each other out, resulting in a purely resistive circuit. This frequency can be calculated using the formula 1/2π√(LC), where L is the inductance and C is the capacitance of the circuit.

5. How can I calculate the total impedance of an RLC AC circuit?

The total impedance of an RLC AC circuit 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. This impedance represents the overall resistance to the flow of current in the circuit and is used to calculate the current and voltage in the circuit.

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