# Circuits - AC circuits / phasor

• wcjy
In summary, the conversation discusses a question about finding the equivalent impedance and magnitude of current without units, and the need to account for the phase angle of the source. The conversation also touches on using LaTeX and the importance of specifying the phase angle in AC circuits.

#### wcjy

Homework Statement
Given the following circuit with the voltage source V=5 cos(t+θ) and the resistor R1=1.1(Ω) and the inductor L1=0.8(H). The impedance Z_eq of the circuit and the phasor current I can be respectively described as

$$Z_{eq} =a+jb$$
$$I= I_o ∠ Φ$$

Find a, b, and Io in these expressions.
Relevant Equations
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Hi, my school has no answer key provided. and would like to check if this is correct. Thanks!

Hi. It looks like you've correctly found the equivalent impedance and the magnitude of the current (both without units though). However, you'll need to account for the phase angle θ of the source in your Io.

gneill said:
Hi. It looks like you've correctly found the equivalent impedance and the magnitude of the current (both without units though). However, you'll need to account for the phase angle θ of the source in your Io.
From the question, I_o is without phase angle. where I = I_o ∠ Φ. That is why i didn't account for the phase angle.

side note: how do you input latex for like I_o in the text

It's ##I_{0}## [sharp(#) sharp(#) I_{0} sharp(#) sharp(#) ]

wcjy said:
From the question, I_o is without phase angle. where I = I_o ∠ Φ. That is why i didn't account for the phase angle.
Presumably you'll need to specify what ##\Phi## is, no?

gneill said:
Presumably you'll need to specify what ##\Phi## is, no?
i don't need to but is it even possible, since they did not give angle ##\theta##

You need ##\theta## to compute ##\varphi##

wcjy said:
i don't need to but is it even possible, since they did not give angle ##\theta##
You can specify ##\Phi## in terms of ##\theta## and the impedance's angle.

DaveE
gneill said:
You can specify ##\Phi## in terms of ##\theta## and the impedance's angle.
Yes, phase shift matters in AC circuits.

## 1. What is an AC circuit?

An AC circuit is a type of electrical circuit that uses alternating current (AC) to deliver power. Alternating current refers to the flow of electricity that constantly changes direction, usually at a specific frequency. AC circuits are commonly used in household and industrial electrical systems.

## 2. What is a phasor in relation to AC circuits?

A phasor is a representation of the amplitude and phase of an AC circuit. It is a complex number that is used to simplify the analysis of AC circuits by converting the time-varying quantities into a single complex quantity. Phasors are often represented as vectors in a polar coordinate system.

## 3. How do you calculate the impedance of an AC circuit?

The impedance of an AC circuit is calculated using the formula Z = R + jX, where R is the resistance and X is the reactance. Reactance is the opposition to the flow of electricity caused by inductance or capacitance in the circuit. The impedance of an AC circuit is measured in ohms (Ω).

## 4. What is the difference between series and parallel AC circuits?

In a series AC circuit, the components are connected in a single loop, with the same current flowing through each component. In a parallel AC circuit, the components are connected in multiple branches, with the voltage across each component being the same. Series circuits have a single path for current flow, while parallel circuits have multiple paths.

## 5. How do you analyze AC circuits using phasors?

To analyze AC circuits using phasors, the following steps are typically followed:

• Convert all time-varying quantities (such as voltage and current) into phasor form using the appropriate conversion equations.
• Draw a circuit diagram with the phasors representing the amplitude and phase of each component.
• Apply Kirchhoff's laws to the phasor circuit to determine the phasor voltage and current at each point in the circuit.
• Convert the phasor voltages and currents back into time-domain quantities using the inverse conversion equations.
• Analyze the time-domain quantities to determine the behavior of the AC circuit.