Why Did They Add 2π When Shifting AC Circuits?

In summary, the conversation discusses a problem regarding a function and its time shift. The question is about finding the minimum number of milliseconds that the function must be shifted to the left, with a given expression for the function. The conversation also touches on the different approaches to solving the problem and the reasoning behind adding 2pi in the book's solution. The answer lies in the interpretation of "shift to the left" and the implication of a positive time shift.
  • #1
cosine
4
0
Hi everyone,
I ran into the following little problem:

Homework Statement


Given v=40 cos(100*pi*t + pi/3), the question is:
what is the minimum number of millisec that the function must be shifted to the left if the expression for v is 40 cos(100*pi*t)


Homework Equations





The Attempt at a Solution


ok, I started with:
40 cos(100*pi*(t+t0) + pi/3) = 40 cos(100*pi*t)
hence 100*pi*(t+t0) + pi/3 = 100*pi*t
the 100*pi*t cancels out on each side and we can solve for t0 but t0 < 0

BUT the book starts with:
40 cos(100*pi*(t+t0) + pi/3) = 40 cos(100*pi*t + 2pi)
and they solved for t0... and t0 is now > 0

My question why they added the 2pi! Although the more I think about it the more it makes sense to me but I'd like to be sure... Is it because we look for the min time but still positive?
If that's the case, what bothers me is: how are we supposed to know ahead of time to add this '2pi'?

Thanks for your answer(s) o:)
 
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  • #2
I think the answer is that they said "shift the function to the left" implying a positive time shift was being looked for.
 
  • #3
Dick said:
I think the answer is that they said "shift the function to the left" implying a positive time shift was being looked for.

Oh my god... you are right, I can't believe I didn't think of it this way... That totally makes sense !:biggrin:

Thx
 

FAQ: Why Did They Add 2π When Shifting AC Circuits?

1. What is an AC circuit?

An AC circuit is an electrical circuit that operates on alternating current (AC) rather than direct current (DC). This means that the flow of electricity constantly changes direction, typically at a rate of 50 or 60 times per second.

2. What are the components of an AC circuit?

The main components of an AC circuit include a power source (such as a generator or power plant), wires or conductors to carry the current, and various electrical components such as resistors, capacitors, and inductors.

3. How does an AC circuit work?

In an AC circuit, the alternating current from the power source causes the electrons to constantly switch direction, creating a flow of electricity. The electrical components in the circuit can alter the properties of the current, such as its voltage or frequency, before it reaches the end of the circuit.

4. What is the difference between AC and DC circuits?

The main difference between AC and DC circuits is the direction of current flow. In AC circuits, the current alternates direction, while in DC circuits, the current flows in only one direction. AC circuits are also typically used for long-distance power transmission, while DC circuits are more commonly used for smaller electronic devices.

5. What are some common applications of AC circuits?

AC circuits are used in a wide variety of applications, including powering homes and businesses, industrial machinery and equipment, and electronic devices such as computers and televisions. They are also essential for long-distance power transmission and are used in many renewable energy sources such as wind and solar power systems.

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