Understanding Inductive Reactance in 60Hz Circuits

In a 100 volt 60Hz circuit, what is the total reactance with a 4 Henry inductor in the circuit?

• A. 1000 ohms
• B. 1200 ohms
• C. 1507 ohms
• D. 2000 ohms

Answer: (C)

To find the total reactance in an AC circuit with a given inductor, the reactance of the inductor can be calculated using the formula: \[ X_L = 2 \pi f L \] where: - \( X_L \) is the inductive reactance in ohms, - \( f \) is the frequency in hertz, - \( L \) is the inductance in henries. Given that the frequency \( f \) is 60 Hz and the inductance \( L \) is 4 Henry, we can substitute these values into the formula: 1. Calculate \( 2 \pi f \): \[ 2 \pi \times 60 \approx 376.99 \, \text{rad/s} \] 2. Now, multiply by the inductance \( L \): \[ X_L = 376.99 \times 4 \approx 1507.96 \, \text{ohms} \] This value is typically rounded to 1507 ohms. This calculation reveals that the total reactance due to the 4 Henry inductor at a frequency of 60 Hz is approximately 1507 ohms, justifying

The world of electrical engineering can sometimes feel like a maze of formulas and concepts, can’t it? But once you wrap your head around it, the beauty lies in its logic. Let’s shift our gaze to a critical component of AC circuits—inductive reactance. Have you ever wondered how circuits respond to changes in electrical current? Specifically, if you're delving into how a 4 Henry inductor behaves in a 100 volt, 60Hz circuit, you’re in for a treat.

To understand the total reactance in this AC circuit, let’s start with the formula for the inductive reactance:

[

X_L = 2 \pi f L

]

Here, (X_L) is the inductive reactance measured in ohms, (f) is the frequency in hertz (in this case, 60Hz), and (L) is the inductance in henries (which is 4 in this scenario). Feeling a little lost? No worries; we'll walk through this together!

First off, let’s calculate (2 \pi f). A quick plug-in gives us:

[

2 \pi \times 60 \approx 376.99 , \text{rad/s}

]

Now, your excitement must be building—what comes next? Multiply this result by the inductor's value. So let’s do the math:

[

X_L = 376.99 \times 4 \approx 1507.96 , \text{ohms}

]

You see, electrical values often get rounded for simplicity. Thus, you’ll find the total reactance due to this 4 Henry inductor at 60Hz neatly rounding off to 1507 ohms. Pretty cool, right? It’s fascinating how such calculations help us decipher the rhythmic dance of currents and voltages in our everyday devices.

By the way, have you noticed how this formula connects all the dots? It emphasizes the interrelationship of frequency and inductance—a concept so fundamental that it resonates across a plethora of electrical applications. Understanding these principles isn’t just for passing exams or tutorials; it’s about empowering yourself in real-world electrical contexts.

Imagine being able to diagnose circuit behavior or just gaining a sleeker understanding of how your home appliances work. Don't you find that incredibly rewarding? So the next time you hear about reactance or inductors, you'll not only recite the formulas but will also appreciate the dance of electromagnetic fields and changing currents.

In conclusion, embracing concepts like Reactance equips future engineers and enthusiasts with not just theoretical knowledge, but practical insight too. This knowledge is what transforms confusion into clarity, don’t you think? So keep asking the big questions, keep crunching those numbers, and relish the wonders of the electrical realm.