الأربعاء، 25 مايو 2011

Current Division in Parallel Circuit of Resistors

      Consider a parallel circuit of tow resistor and connected across a source of V volts.

       Current through R1 is I1 and R2 is I, while total current drawn from source is IT.
...                                IT = I+ I
But                             I= V/R1   , I= V/R2
i.e.                              V =I1 R1  = IR2
...                                 I= I2   (R2/R1)
       Substituting value of I1 in IT,
Key point : In general, the current in any branch is equal to the ratio of opposite branch resistance to the total resistance value, multiplied by the total current in the circuit.
Example : Find the magnitude of total current, current through and if , R1 = 10 Ω , R2 = 20 Ω and V = 50V.

Solution :
      The equivalent resistance of tow is,
                            Req =(R1 R2 ) / ( R1 + R2 ) = (10 x 20)/ (10 + 20) = 6.67 .
                            IT = V/Req = 50/6.67 = 7.5 A
       As per the current distribution in parallel circuit,
It can be verified that  :         IT = I+ I2 .

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