Find Power w/ Phasors: V=IZ in Electrical Engineering

In summary: The answer was given here:In summary, current and voltage are related through the mathematical function V=IZ. However, you can't multiply a current phasor with a voltage phasor to find a power phasor. Power is the product of voltage and current, so you need to use different functions to calculate it.
  • #1
Centurion
1
0
This is not necessarily a HW problem but more me just trying to understand a concept. Why can you multiply phasors together to find Voltage using V=IZ but you can't multiply a current phasor with a voltage phasor to find a power phasor. Instantaneous power is Voltage and Current functions multiplied together, right? So why the seeming discrepancy? Why does it seem to work for some things but not for other things? It's driving me crazy. For example, find the instantaneous power if v(t) = 4cos(pi*t/6) is applied across an impedance Z = 2∠60°. So V = 4∠0° so I = V/Z = 2∠-60°. Just multiplying those phasors together gives me a totally different answer than if I was to convert the phasors to sinusoidal functions and use angle formulas to arrive at an answer. With multiplying phasors, I get 8*cos(pi*t/6 - 60). With angle formulas, I of course get instantaneous power which is 2 + 4*cos(pi*t/3-60) [W]. I'm sorry for my ignorance in this matter. It may be a stupid question but I'm just trying to understand why you can use phasors sometimes but not other times.
 
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  • #2
Hi Centurion! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif
The impedance of reactive elements is not sinusoidal. If you want to work in the time domain, then you must use functions of time and solve the applicable differential equation.

Example: apply v(t) = 4cos(Ѡt) to an inductor of L henries.

v(t) = L · di/dt
4cos(Ѡt) = L · di/dt
di/dt = 1/L · 4cos(Ѡt)

∴ i(t) = 4/L · ∫cos(Ѡt)
= 4/(ѠL) · sin(Ѡt)

For an inductive impedance of 2Ω, reactance ѠL = 2Ω
→ i(t) = 2 sin(Ѡt)

This is identical to the result using phasors.

To determine how the inductor's impedance varies with time, for a sinusoidal excitation,

z(t) = v(t) / i(t)

= 4cos(Ѡt) / (2 sin(Ѡt))

= 2 / tan(Ѡt)

https://www.physicsforums.com/images/icons/icon2.gif This shows for an inductor z(t) swings from -∞ through 0 to ˖∞ periodically and with period half that of the sinusoids' period.
 
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  • #3
Centurion said:
This is not necessarily a HW problem but more me just trying to understand a concept. Why can you multiply phasors together to find Voltage using V=IZ but you can't multiply a current phasor with a voltage phasor to find a power phasor. Instantaneous power is Voltage and Current functions multiplied together, right? So why the seeming discrepancy? Why does it seem to work for some things but not for other things? It's driving me crazy. For example, find the instantaneous power if v(t) = 4cos(pi*t/6) is applied across an impedance Z = 2∠60°. So V = 4∠0° so I = V/Z = 2∠-60°. Just multiplying those phasors together gives me a totally different answer than if I was to convert the phasors to sinusoidal functions and use angle formulas to arrive at an answer. With multiplying phasors, I get 8*cos(pi*t/6 - 60). With angle formulas, I of course get instantaneous power which is 2 + 4*cos(pi*t/3-60) [W]. I'm sorry for my ignorance in this matter. It may be a stupid question but I'm just trying to understand why you can use phasors sometimes but not other times.

A similar question was asked in this thread.
 

Related to Find Power w/ Phasors: V=IZ in Electrical Engineering

1. What is the concept of power in electrical engineering?

The concept of power in electrical engineering refers to the rate at which work is done or energy is transferred in a circuit. It is measured in watts (W) and is calculated by multiplying the voltage (V) by the current (I). Power is an important aspect in electrical engineering as it determines the efficiency and performance of a circuit.

2. How is power calculated using phasors in electrical engineering?

Power can be calculated using phasors in electrical engineering by using the formula P=VI*cos(θ), where P is the power in watts, V is the voltage in volts, I is the current in amperes, and θ is the phase difference between the voltage and current. Phasors, which are complex numbers, are used to represent the magnitude and phase of a sinusoidal waveform, making it easier to calculate power in AC circuits.

3. What is the significance of using phasors in calculating power?

Using phasors in calculating power allows for a more accurate representation of power in AC circuits. This is because phasors take into account the phase difference between the voltage and current, which is not considered in the calculation of power using only the RMS values of voltage and current. Phasors also make it easier to perform mathematical operations, such as addition and subtraction, on sinusoidal waveforms.

4. How do you find the power factor using phasors?

The power factor can be found using phasors by taking the cosine of the phase difference between the voltage and current. This is because the power factor is a measure of how efficiently a circuit uses electrical power. A power factor of 1 indicates that the circuit is using all the power it receives, while a power factor less than 1 indicates that some power is being wasted.

5. How is power factor correction achieved using phasors?

Power factor correction is achieved using phasors by adjusting the phase difference between the voltage and current in a circuit. This can be done by adding capacitors or inductors to the circuit, which can help balance the reactive power and improve the power factor. By improving the power factor, the efficiency of the circuit can be increased, leading to reduced energy consumption and cost savings.

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