Solve Series-Parallel Circuit in Phasor Domain

• Engineering
• slh3410
In summary, the conversation covers solving a circuit with multiple passive elements using symbols and the voltage division equation. The steps include assigning symbols to the elements, solving using the symbols, and using the voltage division equation to find the voltage at a specific node. There is also a discussion on using phasors for multiplication and division.
slh3410

Homework Statement

Where Vs = 120 ∠0° V

Homework Equations

All values are represented in ohms, so they are treated as resistors.

The Attempt at a Solution

Series inductor + resistor

30+j10 ohms = 31.62∠18.435°

Parallel resistor and inductor+resistor

(1/50)= 0.02∠0°, 1/(31.62∠18.435°)= 0.0316∠-18.435°
0.02∠0° + 0.0316∠-18.435° = .050968∠-11.31°
1/(050968∠-11.31°) = 19.62∠11.31°

Series [j10+parallel section]

j10 + 19.62∠11.31° = 23.704∠35.746°

Now the current

120∠0° / 23.704∠35.746° = 5.062∠-35.746°Not sure how to set up the Voltage Division equation. I think I'm doing all the impedance calculations correctly though.

Last edited:
assign symbols to the passive elements, then solve using the symbols. It makes the work easier to follow and easier to correct a mistake.

L1=j10
L2=J10
R1-50 ohm
R2=30 ohm

series inductor + resistor
R2+L2

parallel resistor and inductor+resistor

z1=1/(1/R1 + 1/(R2+L2))

current= vs / (L1 + Z1 )
now plug in #s
Its much easier

now let's get to solving the problem...
Why do you need the current at this point in time?

To set up the voltage division equation you use the same method that you would for all resistors
Vo=Vin*R1/(R1+R2)

so in this case Vn= Vin* Z1 / (L1+Z1)

1 person
I thought I needed the current to eventually use V=IZ, but I guess not.

I followed you up until you got to current. Why is Vs only over L1+Z1? Because you are calculating voltage drops over that outermost loop?

Where did Vn come from as well?

Last edited:
So for multiplication of phasors I use a cross product? What do I do for division?

Last edited:
I have no idea how to solve what I think is the proper voltage division setup:

(120∠0) [(10∠90) / (23.7∠35.75)]

vn is the node between the 2 inductors.
z1 is the parallel combo of the resistor and inductor+resistor. that plus the first inducotor is the total impedance of the circuit.

for division you divide the amplitude and subtract the phase

that is incorrect voltage division.

Vn= Vin* Z1 / (L1+Z1), with vn being that middle node, and z1 being the parallel combo of the resistor and inductor+resistor

What is a series-parallel circuit?

A series-parallel circuit is a type of electrical circuit that contains both series and parallel components. This means that some components are connected in a series, where the current flows through each component in sequence, and other components are connected in parallel, where the current is divided among different paths.

What is the phasor domain?

The phasor domain is a mathematical representation of a circuit in the frequency domain, where complex numbers are used to represent sinusoidal voltages and currents. This allows for easier analysis of circuits with AC (alternating current) sources.

How do you solve a series-parallel circuit in the phasor domain?

To solve a series-parallel circuit in the phasor domain, you can use Kirchhoff's laws, Ohm's law, and the rules for combining series and parallel components. First, convert all components (resistors, capacitors, and inductors) into their phasor equivalents. Then, use Kirchhoff's laws to write equations for the circuit, and solve for the unknown phasors using algebraic manipulations.

What are the advantages of solving circuits in the phasor domain?

Solving circuits in the phasor domain allows for a simpler and more efficient analysis of AC circuits. It eliminates the need for solving differential equations and allows for the use of complex numbers, which simplifies calculations. Additionally, phasor analysis can easily be extended to circuits with multiple AC sources and non-linear elements.

What are the limitations of solving circuits in the phasor domain?

Phasor analysis assumes that all components in the circuit are linear and at steady state, meaning that the voltages and currents do not change over time. This is not always the case in real circuits, so the results obtained from phasor analysis may not be entirely accurate. Additionally, phasor analysis cannot be used for circuits with time-varying sources (such as pulse or square wave signals).

Replies
4
Views
1K
Replies
3
Views
2K
Replies
3
Views
1K
Replies
3
Views
1K
Replies
20
Views
3K
Replies
26
Views
2K
Replies
2
Views
2K
Replies
17
Views
10K
Replies
11
Views
4K
Replies
4
Views
2K