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Why the current in a loop is the same

  1. Dec 21, 2015 #1
    If for example we have in a loop a DC and 2 resistors connected in series, the current in each resistor is different ##I=\frac{V}{R_i}## but we say that the current is ##I=\frac{V}{R_1+R_2}##?

    That means we are looking at the average current in a loop?
     
  2. jcsd
  3. Dec 21, 2015 #2

    BvU

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    Nope. The voltages over the each of the resistors is ##V_i = R_i I_i##, so ##
    I_i=\frac{V_i}{R_i}## but the current in each resistor is the same (it has to go somewhere and it can't go anywhere else), so ##I = I_i\ \ \ \forall i##

    Since ##V_i = R_i I_i = R_i I##, and ##V = \sum V_i## you get ##V = I (\sum R_i) \Rightarrow I = {V\over \sum R_i}##
     
  4. Dec 21, 2015 #3

    cnh1995

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    Voltage across each resistor will be different. The sum of the voltages will be total applied voltage V.
     
  5. Dec 21, 2015 #4

    Dale

    Staff: Mentor

    apply Kirchoff's current law to the node between the two resistors. Is it possible for the currents to be different?
     
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