Effective and mean voltage

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 is 109 V. Determine the effective source voltage.

Result

U1 =  246.625 V

Solution:

R1=103000 Ω R2=197000 Ω R3=200300 Ω  U2=109 V U21=π U2/2=3.1416 109/2171.2168 V U22=U21/2=171.2168/2121.0686 V  I3=U22/R3=121.0686/2003000.0006 A I2=U22/R2=121.0686/1970000.0006 A I1=I2+I3=0.0006+0.00060.0012 A  U11=I1 R1=0.0012 103000125.5567 V  U1=U11+U22=125.5567+121.0686246.6253246.625 VR_{1}=103000 \ Ω \ \\ R_{2}=197000 \ Ω \ \\ R_{3}=200300 \ Ω \ \\ \ \\ U_{2}=109 \ \text{V} \ \\ U_{21}=\pi \cdot \ U_{2}/2=3.1416 \cdot \ 109/2 \doteq 171.2168 \ \text{V} \ \\ U_{22}=U_{21}/\sqrt{ 2 }=171.2168/\sqrt{ 2 } \doteq 121.0686 \ \text{V} \ \\ \ \\ I_{3}=U_{22}/R_{3}=121.0686/200300 \doteq 0.0006 \ \text{A} \ \\ I_{2}=U_{22}/R_{2}=121.0686/197000 \doteq 0.0006 \ \text{A} \ \\ I_{1}=I_{2}+I_{3}=0.0006+0.0006 \doteq 0.0012 \ \text{A} \ \\ \ \\ U_{11}=I_{1} \cdot \ R_{1}=0.0012 \cdot \ 103000 \doteq 125.5567 \ \text{V} \ \\ \ \\ U_{1}=U_{11} + U_{22}=125.5567 + 121.0686 \doteq 246.6253 \doteq 246.625 \ \text{V}



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!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. 75th percentile (quartille Q3)
    statistics Find 75th percentile for 30,42,42,46,46,46,50,50,54
  2. Median and modus
    dice_3 Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell.
  3. Resistance
    Rezistor_2 A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor.
  4. 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?
  5. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  6. Complex number coordinates
    complex_numbers Which coordinates show the location of -2+3i
  7. Seats
    divadlo_2 Seats in the sport hall are organized so that each subsequent row has five more seats. First has 10 seats. How many seats are: a) in the eighth row b) in the eighteenth row
  8. Trinity
    trojka How many different triads can be selected from the group 43 students?
  9. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  10. 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.
  11. Calculation
    pocty How much is sum of square root of six and the square root of 225?
  12. Median
    statistics The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median.
  13. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  14. Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  15. Calculation of CN
    color_combinations Calculate: ?
  16. 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?
  17. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.