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a] Derive an expression for the equivale...

a] Derive an expression for the equivalent resistance of three resistors RI, R2 and R3 connected in a parallel.
b] Fuse of 3 A, 5 A and 10 A are available, calculate and select the fuse for operating electric iron of I kW power at 220 V line.

Text Solution

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It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.
`I =I_(1)+I_(2)`
Let `R_(p)` be the equivalent resistance of the parallel combination of resistors. By applying Ohm.s law to the parallel combination of resistors, we have
`I = V//R_(p)`
On applying Ohm.s law to each resistor, we have
`I_(1)= V//R_(1), I_(2)= V//R_(2)`
From eqns., we have
`V//R_(p) = V//R_(1)+V//R_(2)`
or `1//R_(p)= 1//R_(1)+1//R_(2)`
Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individual resistances.
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Knowledge Check

  • Four resistors R_(1) , R_(2) , R_(3) and R_(4) are connected in parallel . The resultant resistance R is

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