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Finding a Missing Resistor

  1. Jun 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Three resistors are connected as shown in the diagram. If the current from the power supply is 250 mA and the current through R3 is 54 mA, what is the resistance of R3?
    FullSizeRender (2).jpg

    2. Relevant equations
    1/Req= 1/R1 + 1/R2 +1/R3

    V=IR

    3. The attempt at a solution

    First I used the parallel circuit formula of 1/Req= 1/R1+ 1/R2 + 1/R3
    but there are two variables (Req and R3) so I'm not sure how to use that. Also, there's no voltage provided so I'm a bit confused as how to go from here. Any help would be appreciated :)
     
  2. jcsd
  3. Jun 10, 2016 #2

    cnh1995

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    You can see that the resistors are in parallel, meaning voltage across each resistor is equal to the battery voltage.
    Could you calculate voltage of the battery from this information?
    Hint: Ohm's law and resistances in parallel.
     
    Last edited: Jun 10, 2016
  4. Jun 10, 2016 #3
    I had an idea for finding the solution. I was thinking that I could find the total V and then divide it by the total current to find Req and then use that Req in the parallel circuit formula (1/Req= 1/R1 + 1/R2 + 1/R3) to find R3. As for the total voltage of the battery, I know to use V=IR but I'm not sure which numbers to use, since the current of the two known resistors is unknown.
     
  5. Jun 10, 2016 #4

    cnh1995

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    Well, you can combine the two known resistances by finding their equivalent resistance. You can then calculate current through the equivalent resistance and apply Ohm's law.
     
  6. Jun 10, 2016 #5
    So the current for the equivalent resistance of R1 and R2 would be the total current of the circuit with the current of the third resistor subtracted right?
     
  7. Jun 10, 2016 #6

    cnh1995

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    Right.
     
  8. Jun 10, 2016 #7
    I had an idea for finding the solution. I was thinking that I could find the total V and then divide it by the total current to find Req and then use that Req in the parallel circuit formula (1/Req= 1/R1 + 1/R2 + 1/R3) to find R3. As for the total voltage of the battery, I know to use V=IR but I'm not sure which numbers to use, since the current of the two known resistors is unknown.[/QUOTE]
    So I found the voltage and then divided it by the third current (54mA) to find the resistance of the third resistor. I currently have what I believe is the right answer of 333 ohms.
     
  9. Jun 10, 2016 #8

    cnh1995

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    I'm getting 334.something ohms. But your method is correct.
     
  10. Jun 10, 2016 #9
    Alright thank you for your help : )
     
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