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?

Question

Philoid · Accepted 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