Two resistance are given as R 1 = ( 10 ± 0 . 5 ) Ω and R 2 = ( 15 ± 0 . 5 ) Ω . The percentage error in the measurement of equivalent resistance when they are connected in parallel is

Step-by-step solution

For a parallel combination the equivalent resistance is 1 R = 1 R 1 + 1 R 2       . . . ( i ) A general expression for error can be written as x ± ∆ x Differentiating equation (i) d R R 2 = d R 1 R 1 2 + d R 2 R 2 2       . . . ( i i ) The equivalent resistance with R 1 = 10   Ω   &   R 2 = 15   Ω is 1 R = 1 10 + 1 15 ⇒ R = 150 25 = 6 Ω Substituting the above value in equation (ii) d R = 36 0 . 5 100 + 0 . 5 15 × 15 = 0 . 26