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Question

If two resistors R1 and R2 are connected in parallel, the equivalent resistance becomes, 𝑅𝑒𝑞= 𝑅1𝑅2𝑅1+𝑅2 . If 𝑅1=10±0.5 Ω 𝑎𝑛𝑑 𝑅2=4.7±0.2 Ω, find the percentage error in the calculation of the equivalent resistance.

Answer 1

Rp = R1R2/(R1+R2)=10x4.7/(10+4.7)=3.2 Ω

ΔRp/Rp=ΔR1/R1+ΔR2/R2+Δ(R1+R2)/(R1+R2)=0.5/10+0.2/4.7+(0.5+0.2)/(10+4.7)

ΔRp / 3.2=0.14

ΔRp = 0.45

Rp=3.2±0.45 Ω