Question
Sun April 29, 2012 By: Anjali

CURRENT FLOWING THROUGH PARALLEL COMBINATION IS THE SAME IN ALL THE RESISTORS?WHY

Expert Reply
Mon April 30, 2012

The other common connection is two elements in parallel.  Two resistors or any two devices are said to be in parallel when the same voltage physically appears across the two resistors. Schematically, the situation is as shown below.

Note that we have defined the voltage across both resistor (Vp) and the current that flows through each resistor (Ia and Ib) and a voltage variable, Vp, for the voltage that appears across the parallel combination.

        Let's list what we know.

  • The voltage across the two resistors is the same.
  • The current through the parallel combination is given by:
    • Ip= Ia + Ib
  • The currents through the two resistors are given by Ohm's Law:
    • Ia = Vp /Ra
    • Ib = Vp /Rb
        We can combine all of these relations, and when we do that we find the following.
  • Ip= Ia + Ib
  • Ip= Vp /Ra + Vp /Rb
  • Ip= Vp[ 1/Ra + 1/Rb]
  • Ip= Vp/Rparallel
The current get divided in the parallel combination so its same in each branch of equal resistance.
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