Apparent power, impedance and alternating current.

In summary, the problem involves finding the total apparent power of two serially connected impedances with values of π/3 and 0 and apparent powers of 200VA each. Using the equation S = sqrt(P^2 + Q^2), we can find the individual powers, P1 and P2, and then sum them together to find the total apparent power, S. The angle between S1 and S2 is the same as the angle between the impedances. By drawing them on a complex plane, we can determine the length of their sum, which will give us the answer for the total apparent power.
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Homework Statement


Two serially connected impedances one with [itex]\Phi[/itex] = π/3 and other with [itex]\Phi[/itex] = 0. They have apparent power of S1=S2=200VA. Find total apparent power.



Homework Equations



S = sqrt(P^2 + Q^2)



The Attempt at a Solution



so cosPhi = P1/S1. So P1=cosπ/3*200=100W. For other one P2 = cos0*200=200W. How should I continue? Should I find Q too and derive somehow a equation to sum those powers?
 
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  • #2
The complex power, S, delivered to the load is:
S = S1 + S2

and the angle between S1 and S2 is the same as the angle between the impedances.

You want to find the apparent power |S| = |S1 + S2|. If, say:
S1 = 200∠0
S2 = 200∠π/3

Try drawing them in the complex plane. The length of their sum is the answer you're after.
 

FAQ: Apparent power, impedance and alternating current.

1. What is apparent power and how is it different from real power?

Apparent power is the combination of real power and reactive power in an electrical circuit. Real power is the actual power that is used to perform work, while reactive power is the power that is stored and released by reactive elements in the circuit. Apparent power is measured in VA (volt-amperes) and is calculated by multiplying the voltage and current in the circuit. Real power, on the other hand, is measured in watts and is the product of voltage, current, and the power factor.

2. What is impedance and how does it affect alternating current?

Impedance is the total opposition to the flow of alternating current in a circuit. It is a combination of resistance and reactance (a measure of how much a circuit resists changes in current or voltage). Impedance can affect alternating current by limiting the flow of current in the circuit, causing voltage drops and changes in the phase relationship between voltage and current. It also determines the amount of power that can be delivered to a load.

3. How is impedance related to frequency in an AC circuit?

In an AC circuit, the impedance is directly proportional to the frequency. This means that as the frequency increases, the impedance also increases. This is because higher frequencies cause the reactive components in the circuit (such as capacitors and inductors) to have a greater effect on the overall impedance. This is why impedance is often represented as a complex number, with a real part (resistance) and an imaginary part (reactance).

4. What is the power factor and why is it important?

The power factor is the ratio of real power to apparent power in an AC circuit. It is a measure of how efficiently the circuit uses the supplied power. A power factor of 1 means that all the supplied power is being used for useful work, while a power factor less than 1 means that some of the power is being wasted. A low power factor can result in higher energy costs and can also cause voltage drops and losses in the circuit.

5. How can impedance be reduced in an AC circuit?

Impedance can be reduced in an AC circuit by using components with lower resistance and reactance values, such as thicker wires or capacitors and inductors with higher capacitance or inductance. Additionally, improving the power factor of the circuit can also help reduce impedance. This can be achieved by adding power factor correction devices or using more efficient equipment. Ultimately, reducing impedance can lead to more efficient power usage and lower energy costs.

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