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Kirchhoff's Voltage Law

  1. Sep 15, 2005 #1
    Hi,

    My question:

    The batteries have emfs of E1=9.0 V and E2= 12.0 V and the resistors have values of R1=25 ohms, R2=18 ohms, and R3=35 ohms.Assuming each battery has internal resistance r=1.0 ohms find the direction and magnitude of the currents.


    ____R1______
    |.....................|
    E1...................|
    |_____R2______|
    |.....................|
    E2...................R3
    |_____________|


    For this problem could I use this equation to find the currents.

    V(ab)=E-Ir and I= V/R

    Is this correct :confused:

    Thank You :smile:
     
  2. jcsd
  3. Sep 15, 2005 #2

    Tom Mattson

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    Since you have not labeled nodes "a" and "b", it's not possible to say.
     
  4. Sep 16, 2005 #3
    Please disregard the ab nodes.

    Thank You
     
  5. Sep 16, 2005 #4

    Tom Mattson

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    OK, even if we disregard the "ab", you still aren't going to solve this with a canned equation. You have to apply Kirchhoff's laws to the problem. I think that the easiest way to solve the problem is by superposition. That is, solve the problem once by deactivating E1 and solve it again by deactivating E2 (deactivated voltage sources are just short circuits). Then you can find the currents in each case and add the results together.
     
  6. Sep 16, 2005 #5
    So it would be

    I=V/R

    I(1)=E1/(R1+R2)

    I(2)=E2/(R1+R3)

    to help find the currents needed
     
  7. Sep 16, 2005 #6

    Tom Mattson

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    No, you have to apply Kirchhoff's laws. This requires some analysis beyond simple plug-and-chug.

    As I was explaining, I think the easiest way to do this problem would be to look at the following two circuits:

    ____R1______
    |.....................|
    E1...................|
    |_____R2______|
    |.....................|
    |....................R3
    |_____________|

    and

    ____R1______
    |.....................|
    |.....................|
    |_____R2______|
    |.....................|
    E2...................R3
    |_____________|

    Find the current through each resistor for both circuits. Then you can add up the results for each circuit to get the current through each resistor when both sources are activated. This is called the principle of superposition, and it works because the element law for resistors (V=IR) is linear.
     
  8. Sep 19, 2005 #7
    Hi,

    I have the currents:

    I(1)=.68 A right
    I(2)=.31 A left
    I93)= .18 A up

    what's next :confused:

    Thank You :smile:
     
  9. Sep 19, 2005 #8

    lightgrav

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    Jena,

    if 0.68 C/sec flows into the solder-spot on the right
    (where R1 joins R2 and joins R3),
    then 0.68 C/sec must flow OUT of that node.
    (you have (0.31 - 0.18)[Amp] = 0.13 C/sec out.)

    Why would I3 flow up? only if E2 is + at bottom.
    But then I2 must be large.

    You Did simplify with series and parallel R's first?
     
  10. Sep 22, 2005 #9
    Hi,

    I tried it again and this time I set equations to find the currents using the loop rule.

    Loop 1:

    E1- I1(R1+r)-I2(R2), where is the r, is the internal resistance

    ____R1___>___
    |....................|
    r.....................|
    E1..................V
    |_____R2_<___|


    Loop 2:
    -E2+I2(R2)+I3(R3+r), again where r is the internal resistance

    ____R2___<___
    ^...................|
    |....................|
    E2..................^
    |_r____R2_>___|

    Is this correct :confused:

    Thank You
     
  11. Sep 23, 2005 #10
    Hi,

    I think I got it now, the work is below.

    1. Set up loops

    Loop 1: E1-(R1+r)(I1)-R2(I2)=0
    9V-(25ohms+1ohms)(I1)-(18ohms)(I2)=0
    9V-(26ohms)(I1)-(18ohms)(I2)=0

    Loop 2: E2-(R3+r)(I3)-R2(I2)=0
    12V-(35ohms+1ohms)(I1)-(18ohms)(I2)=0
    12V-(36ohms)(I3)-(18ohms)(I2)=0

    2. Substitution: Add Junctin equation in: I2= I1+I3

    Loop 1: 9V-(26ohms)(I1)-(18ohms)(I2)=0
    9V-(26ohms)(I1)-(18ohms)(I1+I3 )=0
    9V-(44ohms)(I1)-(18ohms)(I3 )=0
    -(44ohms)(I1)-(18ohms)(I3 )=-9V

    Loop 2: 12V-(36ohms)(I3)-(18ohms)(I2)=0
    12V-(36ohms)(I3)-(18ohms)(I1+I3 )=0
    12V-(54ohms)(I3)-(18ohms)(I1 )=0
    -(54hms)(I3)-(18ohms)(I1)=-12V

    3. Add/Subtract Loop 1 and Loop 2. Solve for I3

    Loop 1:18( -(46ohms)(I1)-(18ohms)(I3 )=-9V)
    Loop 2: -44( -(54hms)(I3)-(18ohms)(I1)=-12V)

    I3=(366 V)/(2052ohms)
    I3=.178 A

    4. Solve for I2, using loop 2

    Loop 2:12V-(36ohms)(I3)-(18ohms)(I2)=0
    12V-(36ohms)(.178 A)-(18ohms)(I2)=0
    I2=.309 A

    5. Sove for I1, using junction equation
    Junction equation: I2=I1+I3
    .309A= I1 +.178A
    .309A -.178 A= I1
    I1 =.131 A

    Is this the correct way to do it :confused:

    Thank You :smile:
     
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