__Chapter 1 - Circuit Variables____1.6 - Power Calculations__

We will be starting off in section 1.6, Power and Energy on page 14.

Power and energy calculations are very important in circuit analysis. This may seem like common sense, but this is so due to the fact that all practical devices have limitations on the amount of power they can take. Therefore, as engineers, it's important to understand these limitations.

Power can be related to voltage an current by means of a simple connection as follows; power is the amount of energy per unit time, and can be expressed as the derivative...

where

p = power in watts

w = energy in joules

t = time in seconds

Notice, a watt (W) is given by joules per second. While this connection is important, in and of its self, it's not very useful . Make it useful, recall from your physics class that voltage can expressed in energy per unit charge...

where

v = voltage in volts

w = energy in joules

q = charge in coulombs

and recall that current can be expressed in terms of charge per unit time...

where

i = current in amperes

q = charge in coulombs

t = time in seconds

Putting these facts together, notice that if the

*dq*terms were canceled would be left with our original definition for power, but merely substituting terms we get something new and useful...where

p = power in watts

v = voltage in volts

i = current in amperes

Now that's more useful. We can now relate the voltage across, and the current through a circuit element to the amount of power that it consumes (positive power) or generates (negative power).

And on that note there is one more important connection that must be made. The sign of power is based on the movement of charge through voltage drops and rises, i.e. as a positive charge moves through a voltage drop, it loses energy. And if it moves through a rise in voltage, it will gain energy. This rule for determining the sign of power is called passive sign convention for power elements. So to sum it up, if current enters the positive terminal, or leaving the negative terminal of any element, power is positive. If current enters the negative, or leaves the positive terminal of an element, the power is negative.

For example, consider the black box below.

If the voltage across the boxes terminals is equal to 12 volts (

*v*= 12V) and the current into it is equal to 3 amps (*i*= 3A), how much power is being absorbed or dissipated inside the black box and what is its sign? What if the voltage is negative? Ill post the answer next lesson.That wraps it up for today's lesson. If you have the book, try problems 1.12, 1.17, and 1.24. For next time, start reading Chapter 2, we are just going to jump right in.

If you have any questions, PLEASE feel free to post them in the comments!

Even though this is a little to hard for me, i love it! It makes me scared of college..

ReplyDeleteand this is why I didnt go to college or uni :D

ReplyDeleteThis just seems a little complicated, but I'm sure with the right education I would know exactly what you're talking about!

ReplyDeleteMy head is spinning...

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ReplyDeletelooking forward for answers ! i'm not sure in my skills

ReplyDelete