3 phase load

Two wattmeters are connected to measuring power in a 3 phase balanced load. Determine the total power and power factor if the two wattmeters read 1000 watts each (1) both positive and (2) second reading is negative


P1 =  2000 W
f1 =  1
P2 =  0 W
f2 =  0


P11=1000 W P21=1000 W  P1=P11+P21=1000+1000=2000 WP_{11}=1000 \ \text{W} \ \\ P_{21}=1000 \ \text{W} \ \\ \ \\ P_{1}=P_{11}+P_{21}=1000+1000=2000 \ \text{W}
f1=cosφ1  t1=3 P11P21P11+P21=3 100010001000+1000=0  f1=cos(arctan(t1))=cos(arctan(0))=1f_{1}=\cos φ_{ 1 } \ \\ \ \\ t_{1}=\sqrt{ 3 } \cdot \ \dfrac{ P_{11}-P_{21} }{ P_{11}+P_{21} }=\sqrt{ 3 } \cdot \ \dfrac{ 1000-1000 }{ 1000+1000 }=0 \ \\ \ \\ f_{1}=\cos ( \arctan(t_{1}))=\cos ( \arctan(0))=1
P12=1000 W P22=1000 W  P2=P12+P22=1000+(1000)=0 WP_{12}=1000 \ \text{W} \ \\ P_{22}=-1000 \ \text{W} \ \\ \ \\ P_{2}=P_{12}+P_{22}=1000+(-1000)=0 \ \text{W}
f2=cosφ2  t2=3 P12P22P12+P22=3 1000(1000)1000+(1000)=INF  f2=cos(arctan(t2))=cos(arctan(INF))=0f_{2}=\cos φ_{ 2 } \ \\ \ \\ t_{2}=\sqrt{ 3 } \cdot \ \dfrac{ P_{12}-P_{22} }{ P_{12}+P_{22} }=\sqrt{ 3 } \cdot \ \dfrac{ 1000-(-1000) }{ 1000+(-1000) }=INF \ \\ \ \\ f_{2}=\cos ( \arctan(t_{2}))=\cos ( \arctan(INF))=0

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!

Tips to related online calculators
Do you want to convert time units like minutes to seconds?
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  1. Energy consumption
    elektromer The device is connected to 230V and draws 3.5A current. Power consumption is 1932kJ. How many minutes has this device been in operation?
  2. Effective and mean voltage
    serial-parallel A voltage divider consisting of resistors R1 = 103000 Ω and R2 = 197000 Ω is connected to the ideal sine wave voltage source, R2 is connected to a voltmeter which measures the mean voltage and has an internal resistance R3 = 200300 Ω, the measured value i
  3. Electric input power
    resistor_7 Solve problems related to electric power: a) U = 120 V, I = 0.5 A, P =? b) P = 200 W, U = 230 V, I =? c) I = 5 A, P = 2200W, U =?
  4. Daily temperature
    thermometer The average of daily temperature measurements in one week every day at the same hour was -2.8 °C. All temperatures were measured in different days are different. The highest daily maximum temperature was 2.4 °C, the lowest -6 °C. Determine the options th
  5. AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  6. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  7. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  8. Five harvests
    zrno In the seed company, they know that, out of 100 grains of a new variety, they get an average of 2000 grains after harvest. Approximately how many grains do they get out of 100 grains after five harvests?
  9. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  10. Fish tank
    zebra_fish A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
  11. Calculation of CN
    color_combinations Calculate: ?
  12. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  13. Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  14. Wavelength
    wave_length Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
  15. Father 7
    family_8 Father is 6 times older than his son. After 4 years, the father will only be 4 times older. What are their present ages?
  16. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  17. Population
    population_2 What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?