We appreciate your visit to In a series RC circuit the generator is set to a frequency that is not the resonant frequency It is observed that the ratio of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The frequency of the generator in the series RC circuit is approximately 1.03 Hz.
Explanation:
In a series RC circuit, the resonant frequency is the frequency at which the inductive reactance (XL) and the capacitive reactance (XC) cancel each other out, resulting in a purely resistive circuit. The resonant frequency can be calculated using the formula:
fr = 1 / (2π√(LC))
where fr is the resonant frequency, L is the inductance, and C is the capacitance.
In this case, the resonant frequency is given as 230 H. We can use this information to find the frequency of the generator.
First, we need to determine the values of XL and XC. Since the circuit is not at the resonant frequency, the ratio of XL to XC is observed to be 5.12. This means that XL is 5.12 times greater than XC.
Using the formula for XL and XC:
XL = 2πfL
XC = 1 / (2πfC)
where f is the frequency, we can set up the following equation:
5.12 = XL / XC = (2πfL) / (1 / (2πfC))
Simplifying the equation:
5.12 = 4π²f²LC
Since we know the resonant frequency (230 H), we can substitute the values into the equation:
5.12 = 4π²(230)²LC
Solving for LC:
LC = 5.12 / (4π²(230)²)
Now, we can substitute the value of LC into the formula for the resonant frequency:
230 = 1 / (2π√(LC))
Solving for f:
f = 1 / (2π√(LC))
Substituting the value of LC:
f = 1 / (2π√(5.12 / (4π²(230)²)))
Simplifying the expression:
f ≈ 1.03 Hz
Learn more about RC circuit here:
https://brainly.com/question/34427175
#SPJ14
Thanks for taking the time to read In a series RC circuit the generator is set to a frequency that is not the resonant frequency It is observed that the ratio of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Final answer:
The frequency of the generator in the series RC circuit is approximately 1.03 Hz.
Explanation:
In a series RC circuit, the resonant frequency is the frequency at which the inductive reactance (XL) and the capacitive reactance (XC) cancel each other out, resulting in a purely resistive circuit. The resonant frequency can be calculated using the formula:
fr = 1 / (2π√(LC))
where fr is the resonant frequency, L is the inductance, and C is the capacitance.
In this case, the resonant frequency is given as 230 H. We can use this information to find the frequency of the generator.
First, we need to determine the values of XL and XC. Since the circuit is not at the resonant frequency, the ratio of XL to XC is observed to be 5.12. This means that XL is 5.12 times greater than XC.
Using the formula for XL and XC:
XL = 2πfL
XC = 1 / (2πfC)
where f is the frequency, we can set up the following equation:
5.12 = XL / XC = (2πfL) / (1 / (2πfC))
Simplifying the equation:
5.12 = 4π²f²LC
Since we know the resonant frequency (230 H), we can substitute the values into the equation:
5.12 = 4π²(230)²LC
Solving for LC:
LC = 5.12 / (4π²(230)²)
Now, we can substitute the value of LC into the formula for the resonant frequency:
230 = 1 / (2π√(LC))
Solving for f:
f = 1 / (2π√(LC))
Substituting the value of LC:
f = 1 / (2π√(5.12 / (4π²(230)²)))
Simplifying the expression:
f ≈ 1.03 Hz
Learn more about frequency of the generator in a series rc circuit here:
https://brainly.com/question/34427175
#SPJ14
