Three resistors have the following magnitudes: R1 = 40 Ω ± 10%, R2 = 20 Ω ± 10%, R3 = 10 Ω ± 10%. Determine th

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Three resistors have the following magnitudes: R1 = 40 Ω ± 10%, R2 = 20 Ω ± 10%, R3 = 10 Ω ± 10%. Determine the magnitude of the limiting resultant resistance when all three resistances are connected in series.

Examoogle · Accepted Answer

The correct answer is Option B: 70 \,\Omega \pm 10\%. When components with the same percentage tolerance are connected in series, the resultant percentage error is the weighted average of individual tolerances, which remains equal to the individual tolerance value.

Step-by-Step Solution & Concepts:
Shortcut Trick: When components with the same percentage tolerance are connected in series, the resultant percentage error is the weighted average of individual tolerances, which remains equal to the individual tolerance value.

Formula Used: $$R_{eq} = R_1 + R_2 + R_3$$

Given: Resistors R1 = 40 Ohm +/- 10%, R2 = 20 Ohm +/- 10%, R3 = 10 Ohm +/- 10%.

Steps: Calculate resultant resistance: For resistors in series, add the nominal values.. Determine absolute error: Calculate the absolute error ($\Delta R$) for each resistor: $\Delta R_1 = 40 	imes 0.1 = 4$, $\Delta R_2 = 20 	imes 0.1 = 2$, $\Delta R_3 = 10 	imes 0.1 = 1$.. Calculate percentage error: Calculate the relative error as the ratio of total absolute error to total nominal resistance.

Answer: B is correct because the nominal resistance is 70 Ohm and the combined relative tolerance is 10%.

Exam Tip: This concept of percentage error propagation is identical to measuring the total uncertainty in instruments, which is a key topic in Physics measurement chapters.

Examoogle · Answer

Option A: 70 \,\Omega \pm 30\%

Examoogle · Answer

Option C: 70 \,\Omega \pm 3.33\%

Examoogle · Answer

Option D: 70 \,\Omega \pm 0.1\%

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