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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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In summary: The household AC voltage is not constant, it changes between 162 V and -162 V, but the average power it supplies to the electric devices is the same as a 230 V DC voltage. In summary, the relationship between AC power and DC power depends on the type of load and the values used for calculations. However, for a purely resistive load, the average power of an AC circuit can be equated to the power of a DC circuit, and the rms values of AC voltage and current can be equated to the voltage and current of a DC circuit. This is because the rms values represent the hypothetical values of voltage and current that would dissipate the same average power on the same resistor

- #1

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Something on the lines of, for example:

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

Thank you.

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- #2

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What do you mean by AC power and DC power?

ehild

ehild

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

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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Andrew Mason said: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?

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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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ehild said: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?

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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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ehild said:

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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FredericChopin said:

, 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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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.FredericChopin said: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

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The voltage changes from 170 to -170 in every cycle... :tongue2:Andrew Mason said: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

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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.ehild said:The voltage changes from 170 to -170 in every cycle... :tongue2:

ehild

AM

The mathematical relationship between AC power and DC power is based on the concept of power, which is the rate at which energy is transferred. In both AC and DC systems, power is calculated as the product of voltage and current. However, the key difference between the two is that AC power is constantly changing, while DC power remains constant.

AC power, or alternating current power, is a type of electrical current that periodically reverses direction, changing polarity. This means that the voltage and current are constantly changing in magnitude and direction. On the other hand, DC power, or direct current power, flows in one direction only and the voltage and current remain constant.

Yes, AC power can be converted to DC power using a device called a rectifier. A rectifier is an electrical device that converts AC power to DC power by allowing current to flow in one direction only. This conversion is commonly used in electronic devices that require DC power to function.

The main advantage of AC power over DC power is that it can be easily transformed to different voltages using a transformer. This allows for the efficient transmission of electricity over long distances. In contrast, DC power cannot be easily transformed and is generally used for shorter distance applications.

The frequency of AC power does not affect its energy consumption. The energy consumption of AC power is determined by its voltage, current, and power factor. The frequency only affects the rate at which the power is delivered, but not the total amount of energy consumed.

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