1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Potential Difference across a resistance

  1. Nov 1, 2014 #1
    1. The problem statement, all variables and given/known data

    a) Find Req of the circuit
    b) Find the potential difference across resistance R3

    Y0k08ep.png

    2. Relevant equations
    Resistors in parallel = (1/R1 + 1/R2 + 1/R3 + ...)^-1
    Resistors in series = R1 + R2 + R3 + ...

    3. The attempt at a solution

    a)
    R3 and R4 are in parallel --> [ (1/40Ω) + (1/50Ω) ]^-1 = 200/9 Ω
    R2 and R_34 are then in series --> 50Ω + (200/9)Ω = 650/9 Ω
    R1 and R_234 are then in parallel --> [ (1/40) + (650/9) ]^-1 = 25.7Ω

    b)
    This is the part I need help with as I'm clueless on even how to start. Any guide is appreciated.
     
  2. jcsd
  3. Nov 1, 2014 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    How is the potential split between two resistances in series?
     
  4. Nov 1, 2014 #3
    In series, the potential is equal to the sum of the individual voltages I recall. So Vtot = V1 + V2 + ...
     
  5. Nov 1, 2014 #4

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes, and how would you find the individual voltages?
     
  6. Nov 1, 2014 #5
    Using Ohm's Law, V = IR --> I would say find the current first. So I = V/R.
    Vtotal = 10 V here --> I = 10V/Rtotal = 10/26
    V1 = I(R1)
    V2 = I(R2)
    V4 = I(R4)
    Then, V3 = I(R3) = 15.38 V

    The answer however is 5.5 V.
     
  7. Nov 1, 2014 #6

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The current you have computed is the total current through the equivalent circuit, not the current through R3.
     
  8. Nov 1, 2014 #7
    I am unsure of how to find the current through R3, the individual resistor.
     
    Last edited: Nov 1, 2014
  9. Nov 1, 2014 #8

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You do not need to. There are several ways of approaching this and the one I had in mind does not rely upon it. Let us try another one: Can you find a relation between the potential across R2 and that across R3?
     
  10. Nov 1, 2014 #9
    Well since R2 and R3 are in series, V23 = V2 + V3
     
  11. Nov 1, 2014 #10

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    And what does it have to equal to?
     
  12. Nov 1, 2014 #11
    Since this is a closed loop, V23 would have to equal 0.
     
  13. Nov 1, 2014 #12

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You can use Kirchoff's laws for sure. However, you are not closing a loop by going across R2 and R3. In order to close it, what other component do you need to cross? (There are two choices, one is simpler than the other...)
     
  14. Nov 1, 2014 #13
    Would need to cross R1 to close it?
     
  15. Nov 1, 2014 #14

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes, or ... (You picked the slightly more complicated choice)

    Alternatively, what is the potential difference across R1?
     
  16. Nov 1, 2014 #15
    I = 10/26
    So V1 = (10/26)(40) = 15.38 V
     
  17. Nov 1, 2014 #16

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    No. All the current does not go through R1 either. You do not need to know the current to know the voltage across R1, it is enough to use Kirchoff's voltage law.
     
  18. Nov 1, 2014 #17
    So would I set V1 + V2 + V3 - 10 = 0 ?
     
  19. Nov 1, 2014 #18

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    No, you are now confusing two of the loops for KVL. Just use one loop at a time.
     
  20. Nov 1, 2014 #19
    For R1: V1 would have to be 10V. Need to clarify that before moving on.
     
  21. Nov 1, 2014 #20

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Correct. So what does this tell you about V2 and V3?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Potential Difference across a resistance
Loading...