Solve AC Circuit Analysis: Calculate Current, Real & Reactive Power

In summary, in a network with two connected nodes, a line with an impedance of 0.5 + 1.2j Ω has a voltage of 33KV at the sending end and 32.5 KV at the receiving end with a lag of 1.5°. The current in the line is 763.45 ∠ -8.38°, and the real and reactive power consumed by the line are 291.5 KW and 700 KVAr, respectively.
  • #1
bd411
39
0

Homework Statement


Two nodes in a network are connected by a line with an impedance of 0.5 + 1.2j Ω. The voltage at the sending end is 33KV and at the receiving end is 32.5 KV with a lag of 1.5° compared to the sending end..

Calculate the current in the line and the real and reactive power consumed by the line itself.


Homework Equations


Standard AC circuit analysis equations.


The Attempt at a Solution



I think I've got this just want to make sure that I'm not doing anything silly with the angles etc:

ISR = VS - VR / 0.5 + j1.2 = (33) - (32.5 ∠ -1.5°) / 0.5 + j1.2

= 763.45 ∠ -8.38°

Real Power consumed = I2*Re(Z) = (763.45)^2 * 1/2 = 291.5 KW
Reactive = I2Im(Z) = (763.45)^2 * 1.2 = 700KVAr

Have I done anything silly? I feel to ask because it seems unusual to me that the reactive power is larger than the real power consumed by the line.

Many thanks !
 
Physics news on Phys.org
  • #2
Looks okay.
 
  • #3
Great, thanks a lot !
 

1. How do you calculate current in an AC circuit?

In an AC circuit, current is calculated using Ohm's law, which states that current (I) is equal to voltage (V) divided by resistance (R). However, since AC circuits have both resistance and reactance, the formula becomes I = V/Z, where Z is the impedance of the circuit.

2. What is the difference between real and reactive power?

Real power, also known as active power, is the portion of power in an AC circuit that does useful work, such as powering a device. It is measured in watts (W). Reactive power, on the other hand, is the power that does not do useful work but is required to maintain the electromagnetic field in an AC circuit. It is measured in volt-amperes reactive (VAR).

3. How do you calculate real and reactive power in an AC circuit?

Real power can be calculated using the formula P = VIcosφ, where V is the voltage, I is the current, and cosφ is the power factor. Reactive power can be calculated using the formula Q = VIsinφ, where sinφ is the reactive power factor.

4. What is the power factor in an AC circuit?

The power factor in an AC circuit is the ratio of real power to apparent power, and it represents the efficiency of the circuit. A power factor of 1 means the circuit is efficient, while a power factor less than 1 means there is some energy loss in the circuit due to reactive power.

5. How do you improve the power factor in an AC circuit?

The power factor in an AC circuit can be improved by using power factor correction techniques, such as adding capacitors to the circuit or using synchronous motors. These techniques help to reduce the amount of reactive power in the circuit, thereby improving the power factor and making the circuit more efficient.

Similar threads

Engineering AC Circuit Power/impedance question
    • Engineering and Comp Sci Homework Help
Replies
16
Views
3K
Engineering Circuit analysis -- Find active and reactive power in the branch....
    • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
AC Power and Effective Currents
    • Engineering and Comp Sci Homework Help
Replies
8
Views
3K
Coil Voltage/Current: Understand Resistance in Relay Circuits
    • Electrical Engineering
2
Replies
48
Views
4K
Engineering Calculate the maximum power of the resistor in a circuit
    • Engineering and Comp Sci Homework Help
Replies
8
Views
2K
Engineering RL Circuit Power Computation: What Am I Missing in My Solution?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
AC Circuit Analysis: Solving Example with Confusing Concepts
    • Electrical Engineering
Replies
3
Views
1K
Nodal Analysis and Power Balance in AC Circuits
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Engineering How Do You Calculate Apparent and Reactive Power in AC Circuits?
    • Engineering and Comp Sci Homework Help
2
Replies
61
Views
30K
Engineering AC Circuit; find average and reactive power to load (and load V and I)
    • Engineering and Comp Sci Homework Help
Replies
8
Views
4K

Hot Threads

Recent Insights

Back
Top