Question
What is the total resistance of a 10-, a 20-, and a 50-ohm resistor connected in parallel?
Answer Options
- A) 5.9 ohms
- B) 0.17 ohms
- C) 17 ohms
- D) 80 ohms
Correct Answer: A
Explanation
The total resistance (R_T) of resistors in parallel is found by summing the reciprocals of the individual resistances and then taking the reciprocal of that sum: 1/R_T = 1/R_1 + 1/R_2 + 1/R_3.
Using the given values: rac{1}{R_T} = \frac{1}{10\text{ }\Omega} + \frac{1}{20\text{ }\Omega} + \frac{1}{50\text{ }\Omega} = 0.1 + 0.05 + 0.02 = 0.17 \text{ siemens.} Then, R_T = 1 / 0.17 \approx 5.88 \text{ ohms}. The total resistance is 5.9 \text{ ohms}.
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