Quick parallel combination — product-over-sum shortcut Using the product-over-sum rule for two parallel resistances, what is the combined value of 150 Ω and 6800 Ω?

Introduction / Context:Technicians routinely combine two resistors in parallel using the product-over-sum shortcut. This fast mental or calculator method avoids repeatedly applying the reciprocal formula and is ideal for quick checks during design or troubleshooting.

Given Data / Assumptions:

• Two resistors: R1 = 150 Ω and R2 = 6800 Ω.
• They are connected in parallel.
• We seek the equivalent resistance.

Concept / Approach:For two parallel resistors, the equivalent resistance is given by either the reciprocal form or the product-over-sum shortcut: Req = (R1 * R2) / (R1 + R2). This works because 1/Req = 1/R1 + 1/R2 = (R1 + R2) / (R1 * R2).

Step-by-Step Solution:Use product-over-sum: Req = (R1 * R2) / (R1 + R2).Compute product: R1 * R2 = 150 * 6800 = 1,020,000.Compute sum: R1 + R2 = 150 + 6800 = 6950.Divide: Req = 1,020,000 / 6950 ≈ 146.762... Ω.Round to one decimal place commonly used in options: 146.7 Ω.

Verification / Alternative check:Check reasonableness: the equivalent of parallel resistors must be less than the smallest branch (150 Ω). Our result (~146.8 Ω) is slightly less than 150 Ω, which is consistent. Also, because 6800 Ω is much larger than 150 Ω, the equivalent should be only slightly below 150 Ω, matching the computed value.

Why Other Options Are Wrong:

• 150: equals the smaller resistor and ignores the small parallel effect of 6800 Ω.
• 0.006: not a plausible resistance in this context; likely a units mix-up.
• 6800: equals the larger resistor; parallel cannot exceed the smaller branch.

Common Pitfalls:

• Forgetting to divide by the sum after multiplying (using only the product).
• Rounding before the final division, which can skew the result.

Final Answer:146.7