Two resistors of resistances `R_1 = 100 pm 3` ohm and `R_2 = 200 pm 4 ` ohm are connected (a) in series , (b) in parrallel. Find the equivalent resistance of the (a) series combination , (b) parallel combination . Use for (a) the relation `R = R_1 + R_2 and ` for (b) `1/R = 1/(R_1) + 1/(R_2) and (DeltaR')/(R^(,2)) = (DeltaR_1)/(R_1^2) + (DeltaR_2)/(R_2^2)`

Explanation

(a) The equivalent resistance of series combination `R= R_(1) + R_(2) = (100 + -3) "ohm " + (200+- 4)` ohm
`=300 +- 7` ohm
(b) The equivalent resistance of parallel combination
`R.= (R_(1)R_(2))/(R_(1) + R_(2)) = (200)/(3) = 66.7` ohm
Then, from `(1)/(R ),= (1)/(R_(1)) + (1)/(R_(2))`
we get, `(Delta R.)/(R.^(2)) = (Delta R_(1))/(R_(1)^(2)) + (Delta R_(2))/(R_(2)^(2))`
`Delta R.= (R.^(2)) (Delta R_(1))/(R_(1)^(2)) + (R.^(2)) (Delta R_(2))/(R_(2)^(2))`
`= ((66.7)/(100))^(2) 3 + ((66.7)/(200))^(2)4= 1.8`
Then, `R.= 66.7 +- 1.8` ohm (Here, `Delta R` is expressed as 1.8 instead of 2 to keept in conformity with the rules of significant figures).