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1. Resistors in series .
- R1 = 2 ohm .
- R2 = 3 ohm .
- R3 = 4 ohm .
Rs = R1 + R2 +R3 .
Rs = 2 + 3 + 4 .
Rs = 9 ohm .
Resistors in parallel .
- 1/R1 = 2 ohm .
- 1/R2 = 3 ohm .
- 1/R3 = 4 ohm .
1/Rs = 1/R1 + 1/R2 + 1/R3 .
1/Rs = 1/2 + 1/3 + 1/4 .
1/Rs = 6/12 + 4/12 + 3/12 .
1/Rs = 6 + 4 + 3/12 .
1/Rs = 13/12 .
Rs = 1.0833333 ( 3 reoccurring ) .
The answer in your text is wrong .
2.
a.
Two 6 ohm resistors in series and 1 6 ohm resistors is parallel .
- R1 = 6 ohm .
- R2 = 6 ohm .
- R3 = 6 ohm .
Rs1 = R1 + R2 .
Rs1 = 6 + 6 .
Rs1 = 12 .
1/Rs = 1/Rs1 + 1/R3 .
1/Rs = 1/12 + 1/6 .
1/Rs = 1/12 + 2/12 .
1/Rs = 1 + 2/12 .
1/Rs = 3/12 .
1/Rs = 1/4 .
Rs = 4 ohm .
b.
Two pairs of 6 ohm resistors .
1st pair of 6 ohm resistors .
1/Rs = 1/6 + 1/6 .
1/Rs = 1+1/6 .
1/Rs = 2/6 .
1/Rs = 1/3 .
Rs = 3 ohm .
2nd pair of 6 ohm resistors .
1/Rs = 1/6 + 1/6 .
1/Rs = 1+1/6 .
1/Rs = 2/6 .
1/Rs = 1/3 .
Rs = 3 ohm .
So ,
2Rs = 2 × Rs .
2Rs = 2 × 3 .
2Rs = 6 ohm .
Hope this helps you .
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