Sunday, 5 February 2017

Combination of resistors (series and parallel)

Combination of resistors (series and parallel)
In simple circuits with resistors, Ohm's law can be applied to find the effective resistance. The resistors can be connected in series and parallel.
Resistors in series
Let us consider the resistors of resistances R1, R2, R3 and R4 connected in series as shown in figure.

If the potential difference applied between the ends of the combination of 

resistors is V, then the potential difference across each resistor R1, R2, R3 and R4 is V1, V2, V3 and V4 respectively.

By Ohm's law,

Where, RS is the equivalent or effective resistance of the series combination.

Thus, the equivalent resistance of a number of resistors in series connection is equal to the sum of the resistance of individual resistors.
Resistors in parallel
Consider four resistors of resistances R1, R2, R3 and R4 are connected in parallel as shown in Fig. A source of emf V is connected to the parallel combination. When resistors are in parallel, the potential difference (V)across each resistor is the same.

A current I entering the combination gets divided
intothrough  and respectively, such that
By Ohm's law, let  be the effective resistance, then

Thus, when a number of resistors are connected in parallel, the sum of the reciprocal of the resistance of the individual resistors is equal to the reciprocal of the effective resistance of the combination.

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