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

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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.`