How Does Negative Voltage and Current Affect Power Direction in Circuits?

[jegues]

Homework Statement

I've got a gap in my understanding of power in circuit. I have a feeling my problem has something to do with sign convention or something. Anyways, here's the question,

Two electrical devices are connected at an interface shown below(see figure). Using the reference marks shown in the figure, find the power transferred and state whether the power is transferred from A to B or B to A, when v = -33 V & i = -1.2 mA.

Homework Equations

$$P = IV$$

The Attempt at a Solution

Okay, I know that since the current is negative it is simply going in the opposite direction than depicted in the diagram. (See figure) With this I can conclude that the power is being transferred from B to A, correct?

Now for the part I'm more so confused about, the negative voltage. All these means is that the voltage that is being measured has a greater negative potential than the ground node (reference node) right? How do I deal with the negative sign when making calculations in equations such as,

$$P = IV$$

?

Do I simply sneak a negative in like so,

$$P = -IV$$

?

Any clarification on this would be extremely helpful!

Thanks again!

 

[CEL]

Power is voltage times current. A positive sign means that the power is being dissipated at the branch. A negative sign means that the power is being furnished by the branch.

 

[jegues]

Power is voltage times current. A positive sign means that the power is being dissipated at the branch. A negative sign means that the power is being furnished by the branch.

So do I keep the negatives when making my calculations for power using,

$$P = IV$$?

Or do I simply include the negatives for voltage and current in my calculations?

A positive sign means that the power is being dissipated at the branch. A negative sign means that the power is being furnished by the branch.

So if my power ends up being positive then the power will be transferred from A to B, and vice versa, if my power ends up being negative then the power will be gained by device A, meaning that the power is being transferred from B to A, correct?

 

[CEL]

So do I keep the negatives when making my calculations for power using,

$$P = IV$$?

Or do I simply include the negatives for voltage and current in my calculations?

Simply include the negatives of voltage and current.

So if my power ends up being positive then the power will be transferred from A to B, and vice versa, if my power ends up being negative then the power will be gained by device A, meaning that the power is being transferred from B to A, correct?

If your power is negative at A, it will be positive at B. Then the voltage is furnished by A and dissipated at B.
Remember that in the source, the current flows from the minus to the plus terminal. So the power is negative.
In the load, the current flows from the plus to the minus terminal, so power is positive.

 

[jegues]

Simply include the negatives of voltage and current.

So if I was given the same situation with say, v= 12 V and i = -2.2 A

Then,

$$P = IV$$

$$P = (-2.2 A)(12V) = -26.4 W$$

So I have -26.4 W of power, flowing from B to A because my power is negative, correct?

If your power is negative at A, it will be positive at B. Then the voltage is furnished by A and dissipated at B.
Remember that in the source, the current flows from the minus to the plus terminal. So the power is negative.
In the load, the current flows from the plus to the minus terminal, so power is positive.

This part really confused me. How do I know which device I'm measuring from. I make the calculation like I did above, but this doesn't tell me if I'm measuring power at device A or device B.

Can you clarify some more?

EDIT:

If your power is negative at A, it will be positive at B. Then the voltage is furnished by A and dissipated at B.

After reading it over, this part makes perfect sense, but the question and confusion still remains at which device am I measuring the power at? Device A or Device B?

 

[CEL]

So if I was given the same situation with say, v= 12 V and i = -2.2 A

Then,

$$P = IV$$

$$P = (-2.2 A)(12V) = -26.4 W$$

So I have -26.4 W of power, flowing from B to A because my power is negative, correct?

No, you have 26.4 W of power flowing from A to B.

This part really confused me. How do I know which device I'm measuring from. I make the calculation like I did above, but this doesn't tell me if I'm measuring power at device A or device B.

Can you clarify some more?

EDIT:


After reading it over, this part makes perfect sense, but the question and confusion still remains at which device am I measuring the power at? Device A or Device B?

According to your picture, the reference current flows from A to B. So, device A is the reference.

 

[jegues]

No, you have 26.4 W of power flowing from A to B.



According to your picture, the reference current flows from A to B. So, device A is the reference.

If device A is the reference and I obtain a negative power in my calculation,

i.e.

$$P = (-2.2 A)(12V) = -26.4 W$$

Then I should have 26.4 W flowing from B to A. A is asorbing power, correct?

 

[CEL]

If device A is the reference and I obtain a negative power in my calculation,

i.e.

$$P = (-2.2 A)(12V) = -26.4 W$$

Then I should have 26.4 W flowing from B to A. A is asorbing power, correct?

No, it´s the reverse. Power is flowing from A to B.

 

[jegues]

No, it´s the reverse. Power is flowing from A to B.

So does a negative power mean that the reference device is absorbing power, or dissapating power?

If it's absorbing, then the power must be flowing into it correct?

What am I misunderstanding?

EDIT: Here's the source of my confusion.

A positive sign means that the power is being dissipated at the branch. A negative sign means that the power is being furnished by the branch.

This is incorrect. If the power has a positive sign, then power is being absorbed. If the power has a negative sign, then it is supplying power.

Now it makes sense that the power is being transferred from device A to device B.

 

[jegues]

Okay after doing some review on passive sign convention I think I have a better idea at what's going on so I'm going to give a few scenarios a shot.

a) v = 12 V & i = -2.2 A

Here we have 26.4 W of power, and the power is being transferred from A to B.

b) v = -33 V & i = -1.2 mA

Here we have 39.6 mW of power, and the power is being transferred from B to A.

c) v = 15 V & i = 40 mA

Here we have 600 mW of power, and the power is being transferred from B to A.

d) v = -37.5 V & i = -43 mA

Here we have 1612.5 mW of power, and the power is being transferred from B to A.

Is this correct? Do I finally have my head on straight?

 

[CEL]

So does a negative power mean that the reference device is absorbing power, or dissapating power?

If it's absorbing, then the power must be flowing into it correct?

What am I misunderstanding?

EDIT: Here's the source of my confusion.



This is incorrect. If the power has a positive sign, then power is being absorbed. If the power has a negative sign, then it is supplying power.

Now it makes sense that the power is being transferred from device A to device B.

If your device has memory (capacitor, inductor, battery) it absorbs and stores power. If it has no memory (resistor) it dissipates power. In both cases the power is positive.

 

[CEL]

Okay after doing some review on passive sign convention I think I have a better idea at what's going on so I'm going to give a few scenarios a shot.

a) v = 12 V & i = -2.2 A

Here we have 26.4 W of power, and the power is being transferred from A to B.

b) v = -33 V & i = -1.2 mA

Here we have 39.6 mW of power, and the power is being transferred from B to A.

c) v = 15 V & i = 40 mA

Here we have 600 mW of power, and the power is being transferred from B to A.

d) v = -37.5 V & i = -43 mA

Here we have 1612.5 mW of power, and the power is being transferred from B to A.

Is this correct? Do I finally have my head on straight?

Yes, this is correct.