Two resistors R₁ = (20 ± 1) Ω and R₂ = (30 ± 3) Ω are connected in parallel. The maximum percentage error in their equivalent resistance is:
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Two resistors R₁ = (20 ± 1) Ω and R₂ = (30 ± 3) Ω are connected in parallel. The maximum percentage error in their equivalent resistance is:

G1 Physics · Accepted Answer

Use 1/R = 1/R₁ + 1/R₂. Differentiating and taking maximum errors: ΔR/R² = ΔR₁/R₁² + ΔR₂/R₂². Since R = (20×30)/(20+30) = 12 Ω, we get ΔR/R = 12[1/20² + 3/30²] = 12[1/400 + 3/900] = 12(0.0025 + 0.003333...) = 0.07. Hence maximum percentage error = 7%.