Two resistors are measured in a laboratory as R₁ = (20 0.2) R₂ = (30 0.6) If they are connected in parallel, the percentage error in the equivalent resistance is:

Step-by-step solution

The equivalent resistance R_p in parallel is given by: 1 R_p = 1 R₁ + 1 R₂ Calculating the equivalent resistance: R_p = R₁ R₂ R₁ + R₂ = 20 30 20 + 30 = 600 50 = 12 Differentiating the parallel resistance formula to find the error propagation: R_p R_p^2 = R₁ R₁^2 + R₂ R₂^2 Rearranging to find the fractional error in R_p : R_p R_p = R_p ( R₁ R₁^2 + R₂ R₂^2 ) Substituting the given values: R₁ R₁^2 = 0.2 20^2 = 0.2 400 = 1 2000 R₂ R₂^2 = 0.6 30^2 = 0.6 900 = 2 3000 R_p R_p = 12 ( 1 2000 + 2 3000 ) = 12 ( 3 + 4 6000 ) =