What is the Difference Between Active and Reactive Power in A.C. Circuits?

In summary, a 50 VAR capacitor, 1000 W heater, and 500 VA impedance at a power factor of 0.8 lagging are connected in parallel to a 230V, 50 Hz power-supply system. The system's active power is 1400W, reactive power is 250VAR, apparent power is 1422VA, and power factor is 0.98. The average power in a complete cycle is equal to the real power, not the apparent power.
  • #1
zorro
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Homework Statement



A capacitor of rating 50 VAR, a heater of rating 1000 W and impedance rating 500 VA at a power factor of 0.8 lagging are connected in parallel to a 230V, 50 Hz power-supply system.Find

a) The system-active power
b) The system-reactive power
c) The system-apparent power
d) The system-power factor.


The Attempt at a Solution



I don't understand what VAR and VA stand for. What are active and reactive powers?
 
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  • #2
VA is volt amperes, a power unit. VA is used to designate apparent power. VAR is reactive power. Real power is given in watts.

Look up "power triangle".
 
  • #3
ok I understood their meanings.
How do I find out each of them?
 
  • #4
Abdul Quadeer said:
ok I understood their meanings.
How do I find out each of them?

Good question. I'm not sure what the designation "impedance rating 500 VA" means. Does your text give any enlightenment? If it were an apparent power for a given power factor I could understand it, but it's associated with a "1000W" heater. The real power should not be greater than the apparent power (which forms the hypotenuse for the power triangle).
 
  • #5
I just know the answers
1400W, 250VAR, 1422VA, 0.98
 
  • #6
Okay, it's not a "heater of rating 1000W and impedance rating 500VA". It's a heater of rating 1000W, and a separate impedance with an apparent power of 500VA when the power factor is 0.8; They are describing two separate components. That should clear things up nicely, right? :smile:
 
  • #7
Yeah cleared up a little.
I want to ask one thing - the power which we calculate using P = VIcos(phi), where V and I are r.m.s. voltages, is it the apparent power?
 
  • #8
Abdul Quadeer said:
Yeah cleared up a little.
I want to ask one thing - the power which we calculate using P = VIcos(phi), where V and I are r.m.s. voltages, is it the apparent power?

The apparent power (in VA) is on the hypotenuse of the power triangle. Real power (in watts) is the horizontal leg, and reactive power (in VAR) the vertical leg.

VA2 = W2 + VAR2
 
  • #9
You did not get my question.
The average power in a complete cycle is Vr.m.s.Ir.m.s.cosΦ
Is it equal to the apparent power?

EDIT: Got it. That is true power.

Thanks for your help!
 
Last edited:
  • #10
Ah. I get you now. The average (or mean) power is the real component of the power triangle, not the apparent power.
 

Related to What is the Difference Between Active and Reactive Power in A.C. Circuits?

1. What is power in an A.C. circuit?

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

2. How is power calculated in an A.C. circuit?

The formula for calculating power in an A.C. circuit is P = V x I x cosφ, where P is power in watts, V is voltage in volts, I is current in amperes, and cosφ is the power factor. This formula takes into account the phase difference between the voltage and current, which can affect the overall power in the circuit.

3. What is the difference between real power and reactive power in an A.C. circuit?

Real power, also known as active power, is the actual power being used in the circuit to perform work. It is measured in watts (W). Reactive power, on the other hand, is the power that is stored and released by the circuit due to inductance and capacitance. It is measured in volt-amperes reactive (VAR) and does not perform any useful work in the circuit.

4. How does power affect the efficiency of an A.C. circuit?

The power in an A.C. circuit affects its efficiency in two ways. First, a higher power means that more energy is being transferred or used, resulting in a more efficient circuit. Second, a low power factor (cosφ) can lead to a decrease in efficiency due to the storage and release of reactive power. Therefore, it is important to maintain a high power factor for optimal efficiency.

5. How can power be controlled in an A.C. circuit?

Power in an A.C. circuit can be controlled by adjusting either the voltage or current. Lowering the voltage will decrease the overall power, while lowering the current will decrease the real power but may increase the reactive power. Power can also be controlled by using devices such as capacitors and inductors to improve the power factor and reduce reactive power.

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