Two resistors of resistances R1=(100 ±3) Ωand R2=(200 ±4) Ωare connected in parallel. The equiva

step 1 In this question we have two resistance. R1 is given is equal to 100 plus minus 3 -oom and R2 is

Two resistors of resistances R1=(100 ±3) Ωand R2=(200 ±4)...

Two resistors of resistances $R_{1}=(100 \pm 3) \Omega$ and $R_{2}=(200 \pm 4) \Omega$ are connected in parallel. The equivalent resistance of the parallel combination is
(a) $(66.7 \pm 1.8) \Omega$
(b) $(66.7 \pm 4.0) \Omega$
(c) $(66.7 \pm 3.0) \Omega$
(d) $(66.7 \pm 7.0) \Omega$

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Key Concepts

Parallel Resistor Networks

In electrical circuits, resistors can be connected in parallel, meaning they share the same voltage across them. The equivalent resistance of parallel resistors is calculated using the reciprocal formula: 1/Req = 1/R1 + 1/R2 + ... . This configuration always produces an equivalent resistance that is smaller than the smallest individual resistor’s resistance, making it a fundamental concept when designing and analyzing circuit behavior.

Uncertainty Propagation in Circuit Calculations

When resistor values have associated uncertainties, the uncertainty in the derived equivalent resistance must be calculated using uncertainty propagation methods. This typically involves partial derivatives (the propagation of error technique), where the uncertainty in each individual resistor contributes to the overall uncertainty of the computed parallel resistance. Such techniques ensure that the precision of the measurements is adequately reflected in the final result.

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