Basic circit question help Eight different values of resistance can be obtained

Question

Basic circit question help

Eight different values of resistance can be obtained by connecting together three resistors 5.50 ?, 3.00 ?, and 3.30 ? in all possible ways. What are the values in the following situations?

All the resistors are connected in series.
  ?

All the resistors are connected in parallel.
  ?

The 5.50 ? and 3.00 ? resistors are connected in parallel, and the 3.30-? resistor is connected in series with the parallel combination.
  ?

The 5.50 ? and 3.30 ? resistors are connected in parallel, and the 3.00-? resistor is connected in series with the parallel combination.
  ?

The 3.00 ? and 3.30 ? resistors are connected in parallel, and the 5.50-? resistor is connected in series with the parallel combination.
  ?

The 5.50 ? and 3.00 ? resistors are connected in series, and the 3.30-? resistor is connected in parallel with the series combination.
  ?

The 5.50 ? and 3.30 ? resistors are connected in series, and the 3.00-? resistor is connected in parallel with the series combination.
  ?

The 3.00 ? and 3.30 ? resistors are connected in series, and the 5.50-? resistor is connected in parallel with the series combination.
  ?

Explanation / Answer

R1 = 5.5 , R2 =3 , R3 =3.3

All the resistors are connected in series = R1 + R2 + R3 = 11.8

All the resistors are connected in parallel = 1/R1 + 1/R2 + 1/R3 = 0.8181

The 5.50 ? and 3.00 ? resistors are connected in parallel, and the 3.30-? resistor is connected in series with the parallel combination= 5.5x3/(5.5+3) + 3.3 = 5.24

The 5.50 ? and 3.30 ? resistors are connected in parallel, and the 3.00-? resistor is connected in series with the parallel combination. = 5.0625

The 3.00 ? and 3.30 ? resistors are connected in parallel, and the 5.50-? resistor is connected in series with the parallel combination.=7.07

The 5.50 ? and 3.00 ? resistors are connected in series, and the 3.30-? resistor is connected in parallel with the series combination=>

series sum=8.5

therefore total resistance = 8.5x3.3/(8.5+3.3) =2.377

The 5.50 ? and 3.30 ? resistors are connected in series, and the 3.00-? resistor is connected in parallel with the series combination.= 8.8x3/(8.8+3)=2.336

The 3.00 ? and 3.30 ? resistors are connected in series, and the 5.50-? resistor is connected in parallel with the series combination.= 6.3x5.5/(6.3+5.5) =2.936

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