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- 32
- 2
- 0.5
- 16
The question is about resistors connected in series and parallel. It asks for the ratio of the effective resistance when the resistors are connected in series (Rs) to the effective resistance when they are connected in parallel (Rp).
Resistors in series:
When resistors are connected in series, the total resistance is the sum of the individual resistances. In the question, four identical resistors, each with a resistance of 8 ohms, are connected in series. Therefore, the total resistance Rs is:
Rs = R1 + R2 + R3 + R4
Rs = 8 ohms + 8 ohms + 8 ohms + 8 ohms
Rs= 32 ohms
Resistors in parallel:
When resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. In the question, the four identical resistors are now connected in parallel. Therefore, the total resistance Rp is:
1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4
1/Rp = 1/8 ohms + 1/8 ohms + 1/8 ohms + 1/8 ohms
1/Rp = 4/8 ohms
1/Rp = 1/2 ohms
Reciprocate on both sides
Rp = 2 ohms
Ratio of Rs to Rp:
The ratio of Rs to Rp is:
Rs/Rp = 32 ohms / 2 ohms
Rs/Rp = 16
Therefore, the answer to the question is (d) 16.
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