How to Solve Problems Involving AC Voltage Using Integral Calculus

In summary, the conversation discusses finding the mean and r.m.s values of a generated AC voltage using integral calculus. The formula V = 4cos2θ is given and the use of the identity cos^2⁡θ = 1/2(1+cos2θ) is suggested. The equations given are a) for finding the mean value and b) for finding the r.m.s. value over a full cycle. The person asking for help is not sure how to solve the problem and is asking for guidance on where to start.
  • #1
maali5
35
0

Homework Statement



A generated AC voltage has a value given by V = 4cos2θ.

You will need to use the identity cos^2⁡θ = 1/2(1+cos2θ)



Homework Equations



a) Find the mean value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus

b) Find the r.m.s. value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus


The Attempt at a Solution



How should I be able to solve problems like this?

Thanx
 
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  • #2
maali5 said:

Homework Statement



A generated AC voltage has a value given by V = 4cos2θ.

You will need to use the identity cos^2⁡θ = 1/2(1+cos2θ)

Homework Equations



a) Find the mean value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus

b) Find the r.m.s. value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus

The Attempt at a Solution



How should I be able to solve problems like this?

Thanx

Use the formulas for mean and rms and do the integrals. Show us what you get.
 
  • #3
LCKurtz said:
Use the formulas for mean and rms and do the integrals. Show us what you get.

I know the two formulas but please explain to me what to do with it. I am lost.

Give me somewhere to start please.
 
  • #4
maali5 said:
I know the two formulas but please explain to me what to do with it. I am lost.

Give me somewhere to start please.

You start with the formulas. If you know the formulas, they are nothing more than integrals. Do you know how to evaluate integrals?

I don't know how to help you until you show me what formulas you are trying and where you are stuck.
 

FAQ: How to Solve Problems Involving AC Voltage Using Integral Calculus

1. What is the purpose of using calculus in real-world applications?

Calculus is used in real-world applications to model and solve problems involving rates of change, optimization, and approximation. It provides a mathematical framework for understanding and predicting natural phenomena and is crucial in fields such as physics, engineering, economics, and medicine.

2. What are some common examples of real-world applications of calculus?

Some common examples of real-world applications of calculus include predicting the trajectory of a projectile, determining the optimal shape of a bridge or building, analyzing financial markets, and modeling the spread of diseases.

3. How is calculus used in the field of physics?

In physics, calculus is used to describe and analyze the motion of objects, as well as the behavior of physical systems. It is used to calculate velocities, accelerations, and forces, and is essential in studying concepts such as gravity, electromagnetism, and fluid dynamics.

4. Can calculus be applied in business and economics?

Yes, calculus is widely used in business and economics to optimize production processes, determine optimal pricing strategies, and make predictions about market trends. It is also used in finance to calculate interest rates, analyze risk, and develop investment strategies.

5. How does calculus differ from other branches of mathematics?

Calculus is unique in its focus on rates of change and accumulation. Unlike algebra and geometry, which deal with fixed quantities, calculus deals with continuously changing quantities. It is also closely related to the concept of infinity, as it involves taking limits and approaching infinitely small or large values.

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