You have three 2-Ω resistors. List the various resistances you can provide with them.

Expert Answers
thilina-g eNotes educator| Certified Educator

To find the resistances we can provide let's first find out the configurations that we can connect these three resistors.

1) All in series.

Then the equivalent resistance will be `R_1`

`R_1 = 2+2+2`

`R_1 = 6 Omega`

2) Two in series with each other and other one is parallel to other two.

`1/(R_2) = 1/2 + 1/(2+2)`

`1/(R_2) = 1/2 + 1/4 = 3/4`

`R_2 = 4/3 Omega`

3) Two in parallel to each other and other is in series to each other.

The parallel resistors woyld give R' resistance.

`1/(R') = 1/2+1/2`

`R ' = 1 Omega`

`R_3 = 2+1 `

`R_3 = 3 Omega`

4) All three are in parallel to each other.

`1/(R_4) = 1/2+1/2+1/2`

`1/(R_4) = 3/2`

`R_4 = 2/3 Omega`

5) Just two are in series to each other

`R_5 = 2+2`

`R_5 = 4 Omega`

6) Just two are in parallel to each other

`1/(R_6) = 1/2+1/2`

`R_6 = 1 Omega`

7) Just one resistor.

`R_7 = 2 Omega`

 

So the resistances you can have are `2/3 , 1, 4/3, 2, 3, 4 and 6.`