How to find a unknown resistor value in paralell-

Discussion in 'Homework Help' started by ESPguitar, Aug 21, 2005.

  1. ESPguitar

    Thread Starter Member

    May 15, 2005
    16
    0
    Hi,

    Long time since i've been here:)

    I need some help with a calculation..

    I have a resistor in a circuit, it's 30 Ω , i wan't to make that to a paralell resistor with total value 20 Ω ..

    How do i find the unknown resistor value?

    Thanks,

    Robin :)
     
  2. Gorgon

    Senior Member

    Aug 14, 2005
    113
    0
    Hi Robin,

    The formula for the resistance(z) of two parallel resistors( a & b ) is z=a*b/( a+b )

    Solving this on a gives you a=z*b/(b-z) (You then put in z=20 and b=30).

    TOK ;)
     
  3. ESPguitar

    Thread Starter Member

    May 15, 2005
    16
    0
    So this gives me:

    I guess this is what you meant:

    A= R2
    B= R1 (we know it's resistance, 30 Ω )
    Z= Rtot (we know the resistance we wan't the paralell circuit to give us, 20 Ω )


    R2=Rtot*R1/(R1-Rtot)

    So:

    R2=20 Ω *30 Ω /(30 Ω - 20 Ω )

    =60 Ω

    R2=60 Ω

    But i guess that it have to be a more complicated formula for this?

    Exactly like it is a easier way to calculate the total resistance in a paralell circuit with only two known resistor values..

    Rtot= R1+R2/R1*R2

    But if we want to find the total resistance in a paralell circuit with 3 or more resistors we use this formula:

    The resistors value is: R1= 10 Ω , R2= 15 Ω , R3= 20 Ω .

    We choose the voltage to have the same value as the resistor with the highest value in the paralell circuit, the voltage will then be 20 volts.

    I=U/R

    I1=U/R1

    20/20=1A,

    I2=U/R2

    20/15=1,33A,

    I3=U/R3

    20/10=2A

    Itot = I1+I2+I3

    1A+1,33A+2A=4,33A

    R=U/I

    Rtot=U/tot

    20/4,33=4,61 Ω


    The total resistance in the paralell circuit is 4,61 Ω.

    Is there a similiar way to calculate the unknown resistor? Or is it nenessecary to use more than 2 resistor in a paralell circuit at any times?

    Thanks for the help!

    Robin :) ;)
     
  4. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Generally, for resistors in parallel:

    1/Rtot = 1/R1 + 1/R2 + 1/R3 ........

    For many resistors in paralle this is a far easier equation to work with.
     
  5. ESPguitar

    Thread Starter Member

    May 15, 2005
    16
    0
    Ok!

    Thanks for your time and help:)

    Robin
     
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