Explain the equivalent resistance of a series and parallel resistor network.

Explanation

Resistors in parallel: Resistors are in parallel when they are connected across the same potential difference as shown in fig. (a).
In this case, the total current I that leaves the battery in split into three separate paths. Let `I_(1),I_(2)` and `I_(3)` be the current through the resistors `R_(1),R_(2)`and `R_(3)` respectively. Due to the conservation of charge, total current in the circuit is equal to sum of the currents through each of the three resistors.
Since the voltage across. each resistor is the same, applying Ohm.s law to each resistor, we have
`I_(1)=(V)/(R_(1)),I_(2)=(V)/(R_(2)),I_(3)=(V)/(R_(3))`....(2)
Substituting these values in equation (1), we get
`I=(V)/(R_(1))+(V)/(R_(2))+(V)/(R_(3))=V[(1)/(R_(1))+(1)/(R_(2))+(1)/(R_(3))]`,
`I=(V)/(R_(P))`
`(I)/(R_(P))=(I)/(R_(1))+(I)/(R_(2))+(I)/(R_(3))` …….(3)Here `R_(P)` is the equivalent resistance of the parallel combination of the resistors. Thus, when a number of resistors are connected in parallel, the sum of the reciprocal of the values of resistance of the individual resistor is equal to the reciprocal of the effective resistance of the combination as shown in the fig. (b).
Note: The value of equivalent resistance in parallel connection will be lesser than each individual resistance.