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[MUSIC]

Â Welcome back to Linear Circuits, I'm Dr. Harris.

Â The topic of this lesson is power, and by the of this lesson, you should be able

Â to define power, as well as understand how power relates to voltage and current.

Â Power is extremely important when you're designing electronic circuits and

Â devices because of power dissipation,

Â power requirements, so let's look at power and see what it means.

Â This lesson builds upon two things.

Â First is the concept of electric current, which is the quantity of charge that

Â passes through a given area in a specified time, and remember that current is dQ dt.

Â This lesson also builds upon voltage, which is the energy gained or

Â lost by a coulomb of charge, and remember that voltage can be written as dw dQ,

Â or change in energy per coulomb of charge.

Â So building upon those two concepts, what exactly is power?

Â Well remember that a charged particle q flows over time to produce a current

Â 1:08

i, dq/dt, and a voltage is produced by the energy that's either lost or

Â gained by that moving charge, or dw/dq.

Â The power is the rate at which that charges energy(W), changes over time.

Â 1:25

So, power is the rate of a charges energy changing over time, or dw/dt.

Â So if you look at our definitions for current, voltage and power, you see

Â that power can also be expressed as the product of the current and the voltage.

Â If you use the chain rule, you see that dw/dt is

Â the same as dw/dq times dq/dt, or v times i.

Â So power is the product of voltage and current.

Â We're going to use the variable p for power and the unit watts, which has

Â an uppercase W, not to be confused with the lowercase w that we use for energy.

Â 2:09

So I've giving that definition that power is the product of voltage and current.

Â Let's take a short quiz and calculate the power for

Â a known voltage and a known current.

Â Pause the video, solve these problems, and then we'll solve them together.

Â 2:42

We know that power is the product of the current and the voltage.

Â Now in this case the current is going downhill from plus to minus,

Â and as a mnemonic device I always use the sign that I get to first.

Â So a positive 5 amps times 2 volts, or

Â in this case, the power is a positive 10 watts.

Â Now because power is just flowing downhill, meaning the current

Â is flowing downhill, it's going, it's not taking any extra energy for

Â this current to flow from plus to minus, so this power is actually consumed.

Â Positive power is consumed.

Â Now let's consider p2.

Â We know that power is current times voltage, but in this case,

Â we have four amps of current going from minus to plus.

Â So it's taking some energy.

Â The current is going, it's opposing the direction that is really wants to flow.

Â It's flowing uphill, and again, I take the sign that I get to first,

Â which is a minus.

Â So I'll say a (-4A)(3V), or

Â the power is a -12W, and we required some

Â energy to get this current to flow from minus to plus.

Â Which means that, in this case, power is actually generated.

Â 4:14

So by our convention, if the current is flowing downhill from plus to minus,

Â and you have a positive voltage, positive current,

Â then we have a positive power, positive power is consumed.

Â In the other case, power is flowing from minus to plus, so

Â we end up with a negative power.

Â Remember that negative power is generated.

Â Another interesting fact about power, is that the sum of power generated and

Â consumed in a system is zero, because power is the rate

Â of change of energy and energy is always conserved,

Â the sum of power generated and consumed in a system is zero.

Â We know that energy is conserved, we're neither creating or destroying energy,

Â and since power is simply the rate of change in that energy,

Â the sum of power also has to be zero.

Â So take a look at this system.

Â You have an unknown power with three other sources

Â that are generating and consuming 3 watts, -7 watts, and 6 watts.

Â What is Px?

Â Think about it.

Â We have plus 3, plus 6, which is a plus 9, and

Â a -7 which means that PX must be -2,

Â because -2 watts and -7 watts totals -9 watts, and

Â plus 3 watts plus 6 watts equals plus 9 watts.

Â So, 3 and 6 is 9, 2 and 7 is 9.

Â PX must be a -2.

Â 6:11

We know that the sum of the powers, Px is unknown power

Â plus 4 watts plus 8 watts minus 6 watts equals 0.

Â So, 4 and 8 is 12 minus 6 is plus 6,

Â that means that, Px has to be a -6 watts.

Â 7:08

Again, we have some unknown power plus 2

Â watts minus 3 watts plus 4 watts equals 0

Â to a -3 is minus 1 plus 4 is a positive 3.

Â So Px has equal a -3 watts.

Â In this case,

Â we're looking for the current which is power over the known voltage.

Â So we have a -3 watts divided by 2 volts so our current is -1.5 amps.

Â 7:54

The key concepts that we covered in this lesson are first,

Â that power is the rate at which energy changes over time, or dw/dt.

Â It can also be expressed as the product which is most often the form of V and I.

Â Most of the time you use power as the product of a voltage and the current, and

Â finally, the sum of power generated and consumed in a closed system is zero.

Â So if you know all of the power generated or consumed of several of the elements in

Â a system, you can use those to find the power of an unknown element, and

Â you can also use that power to find an unknown voltage, or an unknown current.

Â Thank you.

Â