Q. 20 C4.5( 12 Votes )

Determine the equivalent resistance of networks shown in Fig. 3.31.


Answer :

(a)



It can be observed from the given circuit that in the first small loop, two resistors


of resistance 1 Ω each are connected in series.


Hence, their equivalent resistance = (1 + 1) = 2 Ω


It can also be observed that two resistors of resistance 2 Ω each are connected in series.


Hence, their equivalent resistance = (2 + 2) = 4 Ω.


Now the given circuit diagram can be explained as


Now draw 4 loops each having 2 resistors of 2 Ω and 4 Ω connected in parallel.


Hence Equivalent Resistance Re of each loop is


Re = 4/3 Ω


Since all 4 loops will be connected in series and each loop will have 4/3 Ω resistance


Hence, equivalent resistance of the given circuit is 4 × 4/3 = 16/3 Ω .


(b)


From the given circuit that five resistors of resistance R each are connected in series.


Hence, equivalent resistance of the circuit = R + R + R + R + R = 5R


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