Increase power consumption with a capacitor

In summary, a motor connected to a 120 V/60 Hz power line drawing a 7.60 A current has an average energy dissipation of 840 W. To increase the power factor to 1.0, a series capacitor with a capacitance of 431 microF needs to be added. This can be found by calculating the series resistance of the motor using the formula P = R*I^2 and the total impedance using Z = U/I, then finding the reactance of the motor using Z=(R^2+X^2)^1/2 and adding a series capacitor with a reactance equal and opposed to the motor's reactance. It is important for the capacitor to be in parallel, not in series.
  • #1
eastoak
4
0

Homework Statement


A motor attached to a 120 V/60 Hz power line draws an 7.60 A current. Its average energy dissipation is 840 W.

How much series capacitance needs to be added to increase the power factor to 1.0? (in micro F)

Homework Equations



Don't know which to use at all.

The Attempt at a Solution



An equation would be just a helpful thanks.
 
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  • #2
Define power factor. (that goes into #2).

Are you sure they are asking for a series capacitor?
 
  • #3
Yeah. That is exactly how the question is worded. There isn't a diagram so I assume it is in series.

I think the question asks what would a capicitance on a capacitor be if it were to increase the energy dissipation to 1680W.
 
  • #4
The answer happens to be 431 micoF. Anyone know how that was solved? z=(Rc^2+Xc^2)^1/2 ? omega=2(3.14)60 ?
 
  • #5
I modeled the motor as an inductance with a series resistance. Here is how you can solve it:

Since the reactive component of the motor model (the inductance) doesn't dissipate power it means that those 840W are dissipated by the series resistance of the motor, and you can find this resistance with the formula P = R*I^2.

The total impedance of the motor can be found by Z = U/I

As you said Z=(R^2+X^2)^1/2. You have Z and R so you can find X.

The power factor is defined as the ratio between active power and apparent power, apparent power being the module of the complex power (which has the active power as real part and the reactive power as the imaginary part). So in order to have the power factor 1 you need to have zero reactive power. This means that the reactance of the motor (the X you calculated) must be equal and opposed to the reactance of the series capacitor you have to add.
 
  • #6
Here is a good overview of the power factor: http://www.ibiblio.org/obp/electricCircuits/AC/AC_11.html
 
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  • #7
I'll take a look at the link.

thanks for the reply.
 
  • #8
not series parallel

you are using the cap to store the active power from inductor effect of the motor windings and supply it back as reactive power. so the capacitor has to be in parallel
 
  • #9
rockstar said:
you are using the cap to store the active power from inductor effect of the motor windings and supply it back as reactive power. so the capacitor has to be in parallel

Thank you! It just made now sense at all in series.
 

1. How does a capacitor increase power consumption?

A capacitor increases power consumption by storing electrical energy in an electric field. When the capacitor is connected to a circuit, it releases this stored energy, which increases the power consumption of the circuit.

2. Can a capacitor be used to improve the performance of a device?

Yes, a capacitor can be used to improve the performance of a device by providing a quick burst of energy when needed, such as during sudden power surges or peaks in demand.

3. Is there a limit to how much power consumption can be increased with a capacitor?

Yes, there is a limit to how much power consumption can be increased with a capacitor. This limit is determined by the size and type of capacitor used, as well as the power source and circuit it is connected to.

4. What are the potential downsides of using a capacitor to increase power consumption?

One potential downside of using a capacitor to increase power consumption is that it can cause fluctuations in the power supply, which can affect the performance of other components in the circuit. Additionally, if the capacitor is not properly sized or connected, it can lead to overheating or damage to the circuit.

5. Are there any safety concerns when using capacitors to increase power consumption?

Yes, there are safety concerns when using capacitors to increase power consumption. Capacitors can store a large amount of energy, which can be dangerous if not handled properly. It is important to follow proper safety precautions when working with capacitors, such as discharging them before handling and using appropriate protective equipment.

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