Two resistances are given as R₁ = (10 ± 0.5) Ω and R₂ = (15 ± 0.5) Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is:
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Question

Two resistances are given as R₁ = (10 ± 0.5) Ω and R₂ = (15 ± 0.5) Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is:

G1 Physics · Accepted Answer

For two resistors in parallel, R = R₁R₂/(R₁ + R₂) With R₁ = 10 Ω and R₂ = 15 Ω: R = (10×15)/(10+15) = 6 Ω For maximum fractional error in a parallel combination: ΔR/R = (ΔR₁/R₁) + (ΔR₂/R₂) − [Δ(R₁+R₂)/(R₁+R₂)] Using ΔR₁ = ΔR₂ = 0.5 Ω: ΔR/R = 0.5/10 + 0.5/15 − 1.0/25 = 0.05 + 0.0333 − 0.04 = 0.0433 Percentage error = 4.33%. Hence option B follows.