Q. 20 B4.6( 12 Votes )

Given the resistances of 1Ω, 2Ω, 3Ω, how will be combine them to get an equivalent resistance of (i) (11/3) Ω (ii) (11/5) Ω, (iii) 6 Ω, (iv) (6/11) Ω?

Answer :

(i)


The resistance of the given resistors is,


R1 = 1 Ω , R2 = 2 Ω , R3 = 3 Ω


Connect 2 Ω and 1 Ω resistor in parallel and 3 Ω resistor in series to them


Equivalent resistance R’ is {(2 × 1)/(2 + 1)} + 3


Hence R’ is equal to 11/3 Ω


(ii)


Now connect 2 Ω and 3 Ω resistor in parallel and one Ω resistor in series to it


Equivalent Resistance R” = {(2 × 3)/(2 + 3)} + 1


R” = 11/5 Ω


(iii)


Now connect all three resistor 1 Ω 2 Ω and 3 Ω in series


Hence total resistance R”’ is 1 + 2 + 3 = 6 Ω


(iv)


Now connect all three resistors in parallel;


Equivalent Resistance is R”” = (1 × 2 × 3)/(1 × 2 + 2 × 3 + 3 × 1)


R”” = 6/11 Ω


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