Equivalent Resistance Calculator
This interactive simulation demonstrates how to calculate equivalent resistance for series and parallel combinations with error propagation, based on Example 2.10 from Physics textbooks.
Series Combination
Parallel Combination
R₁
R₂
Series Combination Formula:
R = R₁ + R₂
ΔR = ΔR₁ + ΔR₂
R = R₁ + R₂
ΔR = ΔR₁ + ΔR₂
Series Combination Result
R₂
R₁
Parallel Combination Formula:
1/R' = 1/R₁ + 1/R₂ ⇒ R' = (R₁ × R₂)/(R₁ + R₂)
ΔR' = R'² × (ΔR₁/R₁² + ΔR₂/R₂²)
1/R' = 1/R₁ + 1/R₂ ⇒ R' = (R₁ × R₂)/(R₁ + R₂)
ΔR' = R'² × (ΔR₁/R₁² + ΔR₂/R₂²)
Parallel Combination Result
Example 2.10 Solution:
(a) Series combination: R = (100 ± 3)Ω + (200 ± 4)Ω = 300 ± 7Ω
(b) Parallel combination:
R' = (100×200)/(100+200) = 20000/300 = 66.7Ω
ΔR' = (66.7/100)²×3 + (66.7/200)²×4 = 1.33 + 0.44 = 1.8Ω
Final result: R' = 66.7 ± 1.8Ω
