Four resistors all have resistance 30 W . Find all the possible equivalent resis

Question

Four resistors all have resistance 30 W . Find all the possible equivalent resistnaces that can be created (there are ten) and list them from largest to smallest equivalent resistance.

The largest equivalent resistance is ?
The 2nd largest equivalent resistance is ?
The 3rd largest equivalent resistance is ?
The 4th largest equivalent resistance is ?
The 5th largest equivalent resistance is ?
The 6th largest equivalent resistance is ?
The 7th largest equivalent resistance is ?
The 8th largest equivalent resistance is ?
The 9th largest equivalent resistance is ? .
The smallest equivalent resistance is ?

Explanation / Answer

The largest resistance is when they are in series:
r1+r2+r3+r4 =120

rd, ri, rb, rh, rc, rg, rf, re

2nd largest, 3 in series:

r1+r1+r3 = 90

3rd largest 2 series parallel to 2

r1+r2=60, 1/r3+1/r4=1/15

r = 75

4th 2 in series

r = 60

5th largest3 parallel, 1 series

r123 = 10; r4 = 30

r = 40

6th largest (r1,r2 series) parallel (r3,r4)

1/60+1/60 = 1/r

r = 30

7th largest 3 series, 1 parallel

r123 = 90 ; 1/90+1/30 = 1/r

r =22.5

8th largest 2 parallel

r = 15

9th largest 3 paralle

r = 10

10th largest all parallel

r=7.5

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