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N identical resistors, each of resistance R, when connected in parallel,their effective resistance is Yohm . find the relation between R,X and Y




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Resistance = R
When resistances are connected in parallel, the effective resistance is :
Let there be a voltage source V and N resistors of value R be connected in parallel with that voltage source.  The total current is I.  All resistances have the same voltage difference.  The current is divided equally among all the resistors and the current in each resistance is = V/R.  The currents flow in parallel directions.

  Hence total current is I = N * V/R  =  V / (R/N)
   Hence the effective resistance =  V / I = R/N

  1/Y = 1/R + 1/R + ....+ 1/R    N times.
       = N / R

  Y = R/N

1 5 1
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