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!

Homework Help: Circuit analysis - Potential differences of resistors

  1. Mar 12, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]R_1 = 70 \Omega[/tex], [tex]R_2 = 144 \Omega[/tex], [tex]R_3 = 237 \Omega[/tex], [tex]R_4 = 117 \Omega[/tex], [tex]R_5 = 246 \Omega[/tex]; [tex]V_{ab}=43 V[/tex]
    I am looking for the voltage of each resistor as well as the current passing through each one.

    2. Relevant equations
    Kirchoff's Voltage/Current Laws: The sum of any potential differences across a closed path is zero; current (charge) is conserved, so any current exiting a node is equal to the sum of the currents entering it.
    [tex]V = IR[/tex]
    [tex]I = \frac VR[/tex]

    3. The attempt at a solution
    I know [tex]R_{eq}=339\Omega[/tex]. Thus, [tex]I = \frac VR = \frac{43}{339} = .127 A[/tex].

    [tex]V_5 = I*R_5=.127*246=31.2 V[/tex]

    [tex]V_1+V_2+V_3-V_4=0[/tex]. This is Kirchoff's voltage equation.

    [tex]I_1=I_2=I_3[/tex] b/c current is conserved, so [tex]\frac{V_1}{70}=\frac{V_2}{144}=\frac{V_3}{237}[/tex]. I solve for [tex]V_1[/tex] and [tex]V_2[/tex] in terms of [tex]V_3[/tex]: [tex]V_1=\frac{70V_3}{237}[/tex] and [tex]V_2=\frac{144V_3}{237}[/tex].

    I know the current through [tex]V_3[/tex] and [tex]V_4[/tex] should sum to .127, so: [tex]\frac{V_3}{237}+\frac{V_4}{117}=.127[/tex].

    [tex]V_4=V_1+V_2+V_3[/tex] from above, so plugging in everything I get:

    I solve for [tex]V_3[/tex] and then plug that in to everything else.
    My final answers are: [tex]V_1 = 1.83[/tex], [tex]V_2=3.77[/tex], [tex]V_3=6.2[/tex], [tex]V_4=12.8[/tex], [tex]V_5=31.2[/tex]. However, these answers are incorrect, so I was hoping to find out what I'm doing wrong.
  2. jcsd
  3. Mar 12, 2010 #2


    User Avatar
    Homework Helper

    Hi Baou, welcome to PF.
    Voltage across R4 = V4 = 43 - V5 = 43 - 31.2 = 11.8 V
  4. Mar 12, 2010 #3
    Could you explain how you arrived at that? I don't quite follow...

    Edit: Oh, you mean it should be 11.8 instead of 12.8? Was everything else that I did correct?

    Edit2: Okay, I was just reading the answer on the calculator wrong. Thanks for the help!
    Last edited: Mar 12, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook