Two resistance are expressed as`R_(1) =(3 +- 0.2) Omega` and `R_(2) = (6+- 0.3) Omega`. Which of the following statements) is/are correct?

Options

A. Equivalent resistance in series combination is `(9 +- 0.5) Omega`
B. Equivalent resistance in series combination is `(9 +- 0.1) Omega`
C. Equivalent resistance in parallel combination is `(2+- 0.12) Omega`
D. Equivalent resistance in parallel combination is `(2+-0.5) Omega`

Answer

A, C

Explanation

A) In series combination, `R = R_(1) + R_(2) = 3 + 6 = 9 Omega, therefore R = (9 +- 0.5) Omega`
C) In parallel combination, `1/R = 1/R_(1) + 1/R_(2)` or `R = (R_(1)R_(2))/(R_(1) +R_(2))` or `R= (3 xx 6)/(3 + 6) = 2 Omega`
`1/R = 1/R_(1) + 1/R_(2) rArr -1/R^(2) dR = -1/R_(1)^(2) + -1/R_(2)^(2) dR_(2)`
`rArr (DeltaR)/R^(2) = (DeltaR_(1))/R_(1)^(2) + (DeltaR_(2))/R_(2)^(2) rArr (DeltaR)/4 = 0.2/9 + 0.3/36 = 0.0222 + 0.008333 = 0.03055 xx 4`
`therefore DeltaR = 0.12, therefore R = (2 +- 0.12) Omega`