Phasors for Resistors - Online Tutor, Practice Problems & Exam Prep

In AC circuits, the voltage and current across a resistor are in phase, meaning they reach their maximum and minimum values simultaneously. This is represented by the same angle, ωt, in their phasor diagrams. For example, with an angular frequency of 20 rad/s, after 0.2 seconds, both voltage and current phasors would be at 4 radians (or 229 degrees), indicating they are aligned. Understanding this relationship is crucial for analyzing resistive circuits in alternating current systems.

Phasors for Resistors

Hey guys, in this video, we want to talk about phasers specifically applied to resistors in AC circuits. Alright, let's get to it. Remember, guys, that the voltage and the current across a resistor at any time t are given by these two equations. Okay? These two functions right here. Alright? They are both at the same angle, ωt. Okay? Remember that the angle for any phaser is ωt. Because both of these functions, both of these cosines, have that same angle, they are said to be in phase. Okay? In phase means identical. Alright and I'll show you what this means in the context of the phasers drawn below. The first phaser that I drew is the current through the resistor, and it is at some angle ωt. Next, I drew the voltage across the resistor, which is at that same angle ωt. So when I combine these phasors into a single phaser diagram, I get that the current and the voltage across the resistor line up because they're both at this omega angle, ωt. They are said to be in phase. They line up. Okay. Any 2 phasers that are in phase will always be lined up as they rotate. Okay? So at any time that you choose to measure, it will always be lined up. Sorry. They will always be lined up. Alright? And this is the conclusion that we're going to take away from this video that the voltage across the resistor is in phase with the current through the resistor. Okay, it's very important to remember that.

Now let's do a quick example. An AC source with an angular frequency of 20 inverse seconds is connected to a resistor with the circuit broken. 0.2 seconds after the circuit is completed, draw the voltage phaser and the current phaser. Okay? When the circuit's broken, nothing is happening. The second it's closed, now time starts. Okay? So the question is if we want to draw those phasers, what is the angle that they are going to be at? The angle for the phaser is always going to be ωt. So, this is going to be ω which we are told is 20 inverse seconds times t which we're told is 0.2 seconds. So this is going to be 4 radians which is equivalent to 229 degrees if you just convert quickly between radians and degrees. Alright, so now we know how to draw our phasors. 229 degrees places us in the 3rd quadrant because that's greater than 180 and less than 270. So that's going to put us somewhere around here, 229 degrees. We're going to have a phaser for the current. Sorry, guys. A little technical difficulty. A phaser for the current, and we are also going to have a phaser for the voltage. Sorry if those colors are the opposite of what I used before, the color itself doesn't really matter. And these are in phase. Okay? And you can draw other angles if you want like this angle or this angle. It doesn't really matter as long as whatever angle you choose, it matches up with this angle of 229 degrees. Alright guys, thanks for watching this video. This wraps up our talk about phasors with respect to resistors and AC circuits. Alright? Alright?

A 12 Ω resistor is connected to an AC source. If the resistor's voltage phasor is initially at 0° , and the figure below shows the phasor after 0.04 s, answer the following: 

a) What is the angular frequency of the source? Assume the phasor is on its first rotation. 

b) What does the current phasor diagram look like? 

c) What is the current in the circuit at this point (t = 0.04 ?)?

• A. a) ω = 0.029 s^-1 b) θ = 132^o c) -0.31A
• B. a) ω = 0.029 s^-1 b) θ = 132^o c) 0.31A
• C. a) ω = 18.3 s^-1 b) θ = 42^o c) 0.31A
• D. a) ω = 18.3 s^-1 b) θ = 42^o c) 0.42A

Here’s what students ask on this topic:

What does it mean for voltage and current to be in phase in a resistor?

In an AC circuit, when voltage and current are said to be in phase in a resistor, it means that they reach their maximum and minimum values simultaneously. This is represented by the same angle, ωt, in their phasor diagrams. Essentially, the voltage and current waveforms align perfectly, with no phase difference between them. This characteristic is unique to purely resistive circuits and is crucial for analyzing and understanding the behavior of resistors in AC systems.

How do you draw phasor diagrams for resistors in AC circuits?

To draw phasor diagrams for resistors in AC circuits, follow these steps: First, determine the angular frequency (ω) and the time (t). Calculate the angle θ using θ = ωt. For example, if ω = 20 rad/s and t = 0.2 s, then θ = 4 radians (or 229 degrees). Next, draw the phasor for the current at this angle. Since voltage and current are in phase in a resistor, draw the voltage phasor at the same angle. Both phasors will align, indicating they are in phase.

Why is it important to understand phasors in AC circuits?

Understanding phasors in AC circuits is crucial because they simplify the analysis of AC signals. Phasors convert sinusoidal functions into rotating vectors, making it easier to visualize and calculate the relationships between voltage, current, and impedance. This is especially important in complex circuits with multiple components, as phasors allow for straightforward addition and subtraction of AC signals, aiding in the design and troubleshooting of electrical systems.

What is the relationship between angular frequency and phasor angle in AC circuits?

The relationship between angular frequency (ω) and phasor angle (θ) in AC circuits is given by the equation θ = ωt, where t is the time. Angular frequency, measured in radians per second, determines how quickly the phasor rotates. The angle θ represents the position of the phasor at a specific time. For example, if ω = 20 rad/s and t = 0.2 s, then θ = 4 radians (or 229 degrees). This relationship helps in determining the phase position of voltage and current in AC circuits.

How do you convert radians to degrees in phasor diagrams?

To convert radians to degrees in phasor diagrams, use the conversion factor: 1 radian = 57.2958 degrees. Multiply the angle in radians by this factor to get the angle in degrees. For example, if the angle is 4 radians, the conversion to degrees is 4 × 57.2958 ≈ 229 degrees. This conversion is useful for visualizing and drawing phasor diagrams, as degrees are often easier to interpret.