Show that there are 17 different equivalent resistances that can beformed using

Question

Show that there are 17 different equivalent resistances that can beformed using three resistors. (Use one of three, two of three, orall three.)

Explanation / Answer

we have 3 resistors : R1,R2,R3 if we use 1 resistor => there are C(3,1) = 3 choices =>3 resistances if we use 2 resistors => they can be connect in series orparallel ,in each case,we have C(3,2) =3 choices(to chose 2resistors from 3 resistors we have) => total 2*3 =6 resistances if we use all 3 resistor=> there are 4 case : 3.1) 3 resistors in series => we get 1resistance 3.2) 3 resistors in parallel => we get 1resistance 3.3) 2 resistor in parallel and connect in series with remainresistor => we have C(3,2) choices to chose 2 of 3 resistors andconnect them in parallel => 3resistances 3.4) 2 resistor in series and connect in parallel with remainresistor => similarly , we have C(3,2) choices to chose 2 of 3resistors and connect them in series => 3resistances so the total : N =3+6+1+1+3+3 =17resistances

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