please give me the explanation of this statement "the equivalent resistance is greater than the greatest resistance in the series combination "   
as well as "the equivalent resistance is lesser than the least of all resistance in parallel combination"
pls explain me clearly

Asked by my3shyll | 28th Apr, 2016, 09:54: PM

Expert Answer:

In case of resistors connected in series the resultant resistance of a series combination (equivalent resistance) is the sum of individual resistances.
So, if there are 3 resistors say R1, R2 and R3 connected in series then the equivalent resistance (Rs) is given as 
Rs = R1 + R2 + R3
Thus, we can see that the equivalent resistance is greater than all the resistances, ie., the value of equivalent resistor is greater than the resistor with the greatest value in the series combination.
 i.e. Rs > R1 or R2 or R3
 
In case of parallel combination, the reciprocal of resultant resistance of a parallel combination of resistors (equivalent resistor) is the sum of reciprocals of individual resistances.
begin mathsize 12px style 1 over straight R subscript straight s equals 1 over straight R subscript 1 plus 1 over straight R subscript 2 plus 1 over straight R subscript 3 end style
 
Thus, we can see that the equivalent resistance is lesser than all the resistances, ie., the value of equivalent resistor is lesser than the resistor with the greatest value in the series combination.
i.e. Rp < R1 or R2 or R3

Answered by Yashvanti Jain | 29th Apr, 2016, 07:38: PM

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