Power in AC Circuit: Can Power Be Made Arbitrarily Small?

In summary, in an AC circuit, the average power dissipated is given by P=VIcos(\phi). This means that in a highly inductive or highly capacitive circuit where \phi approaches \pm \pi/2, the power can be made arbitrarily small. Even if a resistor is present, it would not heat up at all. However, adding a capacitor does not reduce the actual value of the real power, which means that in a highly inductive element, there is only a small component of current that is in phase with the voltage. If resistance is added, the phase difference (\phi) will no longer be close to \pi/2, and the power loss will always be I²R.
  • #1
ResonantW
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In an AC circuit, the average power dissipated is given by [itex]P=VIcos(\phi)[/itex]. Does that mean that in a highly inductive, or highly capacitave, circuit where [itex]\phi[/itex] approaches [itex]\pm \pi/2 [/itex], the power can be made arbitrarily small? Even if a resistor were present? Does that mean it wouldn't heat up at all?
 
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  • #2
As a fraction of apparent power, real power can be small, but adding a capacitor doesn't reduce the actual value of the real power.
 
  • #3
ResonantW said:
In an AC circuit, the average power dissipated is given by [itex]P=VIcos(\phi)[/itex]. Does that mean that in a highly inductive, or highly capacitave, circuit where [itex]\phi[/itex] approaches [itex]\pm \pi/2 [/itex], the power can be made arbitrarily small? Even if a resistor were present? Does that mean it wouldn't heat up at all?
In a highly inductive element, there is only a very small component of current that is in phase with the voltage (leaving most to be in phase quadrature). But if resistance is added, then ɸ will no longer be close to Pi/2.

If a current I (RMS) passes through a resistance R, the power loss is I²R. ALWAYS.
 

FAQ: Power in AC Circuit: Can Power Be Made Arbitrarily Small?

1. How is power defined in an AC circuit?

Power in an AC circuit is defined as the rate at which energy is transferred or used in the circuit. It is measured in watts (W) and is a combination of both the voltage and current in the circuit.

2. Can power be made arbitrarily small in an AC circuit?

Yes, power can be made arbitrarily small in an AC circuit by reducing the voltage and/or current in the circuit. This can be achieved by using a transformer or a variable resistor to adjust the voltage and current levels.

3. What is the relationship between power, voltage, and current in an AC circuit?

The relationship between power, voltage, and current in an AC circuit is given by the formula P = V x I, where P is power in watts, V is voltage in volts, and I is current in amps. This means that power is directly proportional to both voltage and current in the circuit.

4. How does power affect the components in an AC circuit?

Power can affect the components in an AC circuit in different ways. A high power level can cause components to overheat and potentially fail, while a low power level can result in the circuit not functioning properly. Therefore, it is important to ensure that the power level is appropriate for the components in the circuit.

5. How can the power level in an AC circuit be controlled?

The power level in an AC circuit can be controlled by using components such as transformers, resistors, and capacitors to adjust the voltage and current levels. Additionally, using a power supply with adjustable settings can also help in controlling the power level. It is important to carefully select and use these components to ensure the power level is within safe limits for the circuit.

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