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Something on the lines of, for example:

Power of AC ... = Power of DC ... ?

Thank you.

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- Thread starter FredericChopin
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- #1

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Something on the lines of, for example:

Power of AC ... = Power of DC ... ?

Thank you.

- #2

ehild

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What do you mean by AC power and DC power????

ehild

ehild

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What do you mean by AC power and DC power????

ehild

I mean power dissipated; as in P = W/t. The power dissipated by an AC and the power dissipated by a DC.

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Andrew Mason

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For a DC circuit with constant voltage V and resistance R, the power is P = V

Something on the lines of, for example:

Power of AC ... = Power of DC ... ?

Thank you.

For AC, you have to define what you mean by voltage since it is changing all the time. You also have to provide details of the load.

If the load is purely resistive (no capacitors or inductors) the power is determined by P = V

AM

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For a DC circuit with constant voltage V and resistance R, the power is P = V^{2}/R = VI

For AC, you have to define what you mean by voltage since it is changing all the time. You also have to provide details of the load.

If the load is purely resistive (no capacitors or inductors) the power is determined by P = V_{rms}^{2}/R = V_{max}^{2}/2R where V_{rms}is the root-mean-square value of the voltage over one cycle - that is to say that the square root of the average/mean of the squares of all the voltages over one cycle.

AM

So... assuming the load is purely resistive, there is no formula that shows the relationship between DC power and AC power?

- #6

ehild

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The power supplied by one source is not related with the power supplied by an other source. DC and AC sources are different sources.

You can speak about instantaneous power and average power. The instantaneous power is product of the instantaneous voltage and current. P(t) = U(t)*I(t).

In case of alternating voltage/current, it has more sense to use the average power, the average of P(t) for a cycle. For sinusoidal voltage and current, P_{av}=IoVo/2 where Io and Vo mean the maximum current/voltage.

ehild

You can speak about instantaneous power and average power. The instantaneous power is product of the instantaneous voltage and current. P(t) = U(t)*I(t).

In case of alternating voltage/current, it has more sense to use the average power, the average of P(t) for a cycle. For sinusoidal voltage and current, P

ehild

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The power supplied by one source is not related with the power supplied by an other source. DC and AC sources are different sources.

ehild

Hm... Ok. So would it be wrong to say:

P

, assuming the load is purely resistive, or:

I

Let me elaborate.

Let's say, for example, there is a DC circuit with a 2 Ω resistor which dissipates 100 W of power. There is also another circuit - an AC circuit - with the same resistor dissipating the same power.

Using the power equation, we know that there is 7.07 A of current passing through the DC circuit. Is it incorrect to say, therefore, that the average (RMS) current passing through the AC circuit is equal to 7.07 A?

- #8

ehild

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We do not use the term "rms power", but average power. On a resistor R, and current I(t)=Io sin(wt), the power is P(t)=(Iosin(wt))

It is said that the rms value of the AC current is equal to that DC current which would dissipate the same power on a resistor as the AC current in average.

ehild

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We do not use the term "rms power", but average power. On a resistor R, and current I(t)=Io sin(wt), the power is P(t)=(Iosin(wt))^{2}R, and the average of the current is Io^{2}/2. Plot it and you will see. So the average power is P_{av}=RIo^{2}/2. You can introduce the rms current which is I_{rms}=Io/√2, then you have the same formula for the average power you would get in case of I_{rms}=Io/√2 DC current. P_{av}=I_{rms}^{2}R.

It is said that the rms value of the AC current is equal to that DC current which would dissipate the same power on a resistor as the AC current in average.

ehild

Ah... I understand.

So I

, for a current flowing through a resistor.

Can you extend that, therefore, and say:

So P

, and:

V

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- #10

ehild

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, for a current flowing through a resistor.

Can you extend that, therefore, and say:

So P_{AVERAGE}of AC = P of DC

, and:

V_{RMS}of AC = V of DC in the same situation?

Well, it is about that. The rms value of the AC voltage/ current is the value of a hypothetical voltage/current that would dissipate the same average power on the same resistor.

So you can use P=UI=I

The voltage of AC sources are given with their rms value. In my country, the household supply is 230 V, the frequency is 50 Hz. That means maximum voltage of 230√2=162 V. The time dependence of voltage is U(t) = 162 sin(100πt).

ehild

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Thank you very much.

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Andrew Mason

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Just to add to what ehild has said, power is the rate at which energy is delivered by electrical means. What you want to ask is not about the relationship between DC and AC power. Rather, it is about how to measure the rate at which energy is delivered by an AC source.So... assuming the load is purely resistive, there is no formula that shows the relationship between DC power and AC power?

If you have a sinusoidal AC voltage with maximum (peak) voltage V

V

So, for example, when we refer to a household voltage being 120 VAC we really mean it is 120 Vrms. The voltage actually ranges from about 170 volts to 0 twice every cycle.

AM

- #13

ehild

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The voltage changes from 170 to -170 in every cycle... :tongue2:So, for example, when we refer to a household voltage being 120 VAC we really mean it is 120 Vrms. The voltage actually ranges from about 170 volts to 0 twice every cycle.

AM

ehild

- #14

Andrew Mason

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Yes. I was referring to the magnitude of the voltage. I should have said the magnitude of the voltage ranges from 170 volts to 0 twice in every cycle.The voltage changes from 170 to -170 in every cycle... :tongue2:

ehild

AM

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