Question
What is the approximate total resistance of a 100- and a 200-ohm resistor in parallel?
Answer Options
- A) 300 ohms
- B) 150 ohms
- C) 75 ohms
- D) 67 ohms
Correct Answer: D
Explanation
The total resistance (R_T) of two parallel resistors (R_1 and R_2) can be quickly calculated using the product-over-sum formula: R_T = (R_1 \times R_2) / (R_1 + R_2). This formula is often faster for exactly two resistors than the reciprocal method.
Using R_1 = 100 \text{ ohms} and R_2 = 200 \text{ ohms}: R_T = \frac{100 \text{ }\Omega \times 200 \text{ }\Omega}{100 \text{ }\Omega + 200 \text{ }\Omega} = \frac{20000}{300} \approx 66.67 \text{ ohms.} The approximate total resistance is 67 \text{ ohms}.
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